Physics-
General
Easy
Question
A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAP0AAADPCAYAAAA+h9daAAAgAElEQVR4nOydeXhU9fX/X7Nk1sySfU/YErYggbCDgogsWkFRsCrFKgruWlvbH9W2Wv32W9f6Vau2KnVDAZHFDREMq4Qk7BAIhC1k35OZJLPf+/sjvZ8mLhCsC5j7ep4+9Zm5985lJud+zuec9zlHI8uyjIqKSrdB+2PfgIqKyg+LavQqKt0M1ehVVLoZqtGrqHQzVKNXUelmqEavotLN0P/YN6Ci8lNBlmWUDLhWe+6up+funamonGf4/X7q6+vxeDycy/IX1ehVVL4DJEmivLycJ554gr179xIKhX7sW/pGVKNXUfkOkGUZl8tFcXExtbW16kqvoqJy7qAavYpKN0M1ehWVboZq9Coq3QzV6FVUuhmq0auodDNUo1dR6WaoRq+i0s1QjV5FpZuhGr2KSjdDNXoVlW6GavQqKt0M1ehVVLoZqtGrqHQzVKNXUelmqEavotLNUI1eRaWboRq9iko3QzV6FZVuhmr0KirdDNXoVVS6GarRq6h0M1SjV1HpZqhGr6LSzVCNXkWlm6EavYpKN0M1ehWVboZq9Coq3QzV6FVUuhmq0auodDNUo1dR6WaoRq+icp7j8Xiora3F7/cjy/IZj1eNXkXlPKe0tJQnn3ySqqoqJEk64/Gq0auonOfU1NSwbt06GhoaumT0+h/gnlRUfhQkSaK5uZkTJ06QkZFBeHh4l88NBoN4vV6ampoIhUJd+qyamhqamppoaGjg1KlT6PVdNy+dTofZbCYqKqrL5yiEQiF8Ph+SJHXJvVeNXuUniyzLFBUV8eCDD/Lyyy+TkZHR5XP9fj+fffYZH374IbIsExYWdsbPamhooKWlhWXLlrF161a02q450rIsI0kSw4YN44477ujyPX5bVKNX+ckiSRJut5tjx47h8XjO6lyv18vRo0fZuXMnF110EU6n84znxMfHM2DAgLP6HFmW8fv9FBQUYDAYzurcb4tq9CoqX4Msy8iyTHJyMrfccgupqanfy+dIkkRrayuPPPIIfr//e/mML6MavYrKN6DRaDAYDNjtdiIjI7+Xz5AkibCwMAwGAz6f73v5jC+jRu9VVLoZqtGrqHQzVKNXUelmqHt6FZVvgSRJ+Hw+mpub8Xg8JCUlUV1djdvtxuFwEBcXR1tbGw0NDbS2tpKUlITVaj1j6u+HQDV6FZVvQSgU4tChQyxfvpympibuueceXnzxRU6dOkVqaioPPfQQu3bt4v3336eqqoopU6Zw/fXXf28BwbNBNXoVlW+BRqPBarVSVFTEiRMnyM7OZt68ebz//vssXboUjUZDRkYG8+fP5/PPP+eVV16hR48e/OxnP/uxb13d06uofBu0Wi1xcXFYLBZkWWbKlCmkp6czZcoUUlNTKSsrY+LEiaSnpzN58mRcLhdHjx79sW8bUFd6FZVvhUajwWg0YjQasVqtJCcnAxATE0NsbCxarRabzYbNZiM6OppgMEhbW9uPfNftqCu9isp3jEaj+bFv4bSoRq+i0s1QjV5F5Vui6PM7IkkSoVBIvK5U0J1LqEavovItkGWZQCCALMsYDAYCgQCSJOH3+wkGg6KsNhQK4Xa7MRqNaLVagsHgj3znqtGrqHwrJEni0KFDDBw4kAkTJrBp0ybcbjclJSUMGjSI9PR0SkpKcLlcHDx4kNmzZ2Mymdi/f3+XGl18n6jRexWVb4FWq2XQoEFkZGQgSZKI5F988cWMGjUKAKvVilarZerUqUycOBGdTofJZPrRA32q0auofAu0Wi1WqxWr1drpdYPB8JW2XCaT6Ye8tTOiuvcqKt0M1ehVVLoZqtGrqHQz1D29yk+WUChEKBTqclfajijBtkAggNvtpqGh4bu+PaA9C9DS0oLf7//BAnyq0av8ZKmvr+fEiROEh4ej0+nO6lylP15NTQ2PP/44ZrP5e7rL9gfLsWPHyMzM/N4+oyOq0av8ZJBlmZaWFqqrq/n8889Zv3495eXlZGZmntWgC2iPuA8ePBi3243X6z3rh8bZIMsy6enpZ9WX/79BNXqV8xpFGdfc3Ex5eTkHDhzgk08+4dSpU8TFxXH99dczZcoU4uLizuq6BoOBUaNGMWjQoB9ERqvT6TAajd/754Bq9CrnKbIsEwqF8Pv9nDp1ilWrVvHpp59SWlrKiBEjuP/++xk9ejQJCQnf6vrKmKnv063/sVCNXuW8IxQK0draysGDB1m6dCmff/45FouFsWPH8sQTT9CrVy/MZvMPtnKeb6hGr3JeoBSzVFZWsmPHDrZu3UpRURFms5lZs2YxcuRIBg4cSGRk5E9ydf4uUY1e5ZwmEAjg8Xhwu90cOXKEN954QxStzJ49mxkzZpCcnIzNZvva8yVJEtVwOp1OdKP1+XwinWcwGNBqtYRCIbxeL1qtFr1e/5VjlfO1Wi2SJOH1etFoNISFhYkJtX6/n0AgIM7XarXIsozH4/nKsYFAAL/fL15TjvV6vQDidVmWCQaD+Hw+DAbDV471er1nVcSjGr3KOYskSZSVlbFu3TpWrVrFtm3buPDCC1mwYAGXX345MTEx6PX60+a3/X4/hw4doqamhqFDhxITEwNAcXExJ06cIDExkczMTIxGI16vl5ycHAwGA9nZ2URHRwNw7NgxiouLSUpKIjMzE5PJhN/vZ/369ZjNZrKzs4mMjESWZU6ePElhYSFpaWn0798fk8mEz+fj888/x2w2M2TIEHFsWVkZu3btok+fPvTt2xej0Yjf72fTpk3o9XqysrLEsRUVFeTn59OvXz/S09PF/ebm5pKXl3dWJbuq0aucczQ2NlJeXs77779PTk4OwWCQCy64gHvvvZfevXsTHR0tcu+nM3iPx0NtbS3vvPMOZWVlpKSkCKPftm0b69atY+zYsfTr1w+j0UggEOD111/HbDaTnp5OdHQ0siyzd+9eVqxYwbBhw+jXr5+49ttvv43RaKR///7COA8ePMjixYtFeS1Aa2sr7777Lnq9npSUFHFsUVERixcvJiMjg9///vcYDAZcLhcrVqwgEAgQExNDRESEKONdvHgxgwcP5je/+Q0Gg4GmpiZWr15NXl4eHo+ny6u9Rv6xi3tVuj2K+9vQ0EBxcTEFBQVs2rQJv99Pz549mTRpEiNHjiQxMfGMK7vP56OlpYWSkhL27NlDXl4ezc3N3HnnnWLPD1BRUUFraytGo5HY2FgMBgMej4eysjIMBgMOh4OIiAhkWRZDLMxmMzExMZhMJrxeL6Wlpeh0uk4DLuvr62lqasJiseB0OjGZTAQCAcrLy9FqteK6kiTR2NhIXV0d4eHhREREYDabCYVCVFRUIMsyNpsNh8MhRm7X1dXhdDqx2WzCg6ipqWHr1q08/PDDLFmyhEGDBp1x5LW60qv8aIRCIQKBAD6fj8LCQt577z02b95MMBhk8uTJTJ8+naysrG/crytIkkQwGBSBvlWrVrF27VpKS0sJDw+npqaG2267Db1ejyRJaLVa4uPj8Xq9tLW10dLSAoDRaKRv374ABINB3G632HNHRUVhNBqFQRkMBqKjowmFQgA0NDRgs9mIiooS3W9bW1vxeDwAOBwObDabyCgoMQJlCxEIBDAYDISFhZGWliYeXk1NTUB7CrF3797odDpkWcbn89Ha2orVasVms53R6+mIavQqPwqhUIjq6mry8/NZvHgx+/fvJzk5mWuvvZbp06eTmJiI0Wg84xgoWZZxuVzs37+f1atX8+mnn2I0Ghk9ejQPPvggdXV13HzzzTz33HMMHTqUX/ziF6SkpOD1ennyySepqKgQ17Lb7Tz++ONotVpqamp4+eWXqampQZZlwsLCGDBgAHPnzsVqtdLc3Mwf//hHMVNeo9Ewbtw4rrzySkwmE0ePHuW1117D7XaL60+bNo0rr7wSgA0bNrBmzRrxUAgPD+e2224jPT0dWZbJz8/n7bff7nRvs2bNYsiQIXi9Xl566SWOHz+OLMuUlpbicrlU917l3CMUCgkXev369eTl5VFeXk5ycjIXXnghQ4YMoWfPnthsttO6qLIs4/f7qampYfv27WzcuJHi4mLMZjOjR49m2LBhDBgwgPDwcLZt28Ytt9zCokWLGDp0KOHh4RiNRrESdzRKo9FITEwMGo0Gj8dDc3MzwWAQWZbRarUYjUbsdjsGgwG/309dXZ1Y6TUaDTabDbPZjF6vx+v10tLS0mnmvMPhwG63A9Dc3ExbW5sIwBkMBiwWi/Bq3G63WOWV98PDwzGZTKKHfmtrq3hALFy4kCVLlpCZmam69yo/Lorr7XK5qKurIz8/n/fee4+qqiqio6OZM2cOEydOJCYm5itdaDqidJV1u900NjZy5MgRli1bRmFhITqdjkmTJjFz5kzS0tJwOp1Au8us0WgIhUK0tbWJdlUANTU1NDU1YbVaSUxMFHv6AwcOEBYWRlxcHPHx8UD7/r+hoYHw8HBhlLIs09DQII51Op1i/19bW4vD4SA2NlYECI8ePSqCbXa7HZvNht/vp7a2lsjISJxOp2iwefz4cTQaDfHx8YSHhyPLMo2NjRQXFxMbG0tUVBROpxOLxcKpU6dwuVxn96PIKirfE5IkyV6vVz5w4ID88MMPy8OHD5fj4uLkm266Sf7ggw/khoaGLl8nEAjI1dXV8ssvvyxfdtllcmxsrDxt2jT5H//4h3zixImvPc/v98sff/yxrNVq5aSkJDknJ0e899BDD8lJSUnyzTffLNfW1sqyLMsnT56UU1JS5L59+8pbtmwRn/3YY4/JcXFx8ty5c+XKykpZkiS5rKxMTkpKkgcNGiTn5eXJsizLwWBQfvbZZ+WoqCj5lltukSsqKuRQKCRXVFTIPXr0kIcNGyZv3bpVDoVCss/nk1999VXZ4XDId9xxh1xRUSEHg0G5srJSzsrKkocPHy5v3rxZ9vv9cltbm/zGG2/IZrNZ/tWvfiVXVlbKgUBALikpkS+88ELZbDbL8fHxckFBgezz+c74faruvcp3TigUorGxkcOHD/Pmm2+yadMmoqKimDBhAjNnziQxMRG73Y7JZDpt9Zr876q5kpISVq1axdKlSzGZTPTr1485c+bQv39/HA4HZrP5a13aQCBATk4ON998M4sWLWLUqFE4HA6gfaVXovcxMTGEhYXh9XopLy8nLCwMh8Mhjq2trRXR+6ioKOHel5WVodfrcTqd2O12sfo3NTURHh4uVu9gMEh5eTk6nU5E3yVJorm5mfr6euH2GwwGEb3XaDRERERgtVpF3KKmpobIyEjsdjthYWEEg0Gqq6vZsmULDz/8MO+++67q3qv8sLhcLmpra9m1axfbt29n//79hIeHM3PmTCZNmsTAgQOJioo6Y6S5ra2NpqYmDhw4QF5eHjt37sTn8zFu3DjRbTYmJkb0kj8ToVCIqqoqKioqMBgMmEwmHA4Hra2tHD9+XLjTUVFR9O3bF41GQ0tLCwcPHqSpqQlJktDr9URFRREREQG0b1vq6+vx+XycOnUKjUZDnz59iIiIwOl00tLSQlFRkYgZaLVaevfuLbYHdXV1lJaW4vF4qKqqIjw8nNTUVCIjI0lNTaWqqoq9e/eK4JzVaqV3795YrVYCgQClpaWUlZUhSRINDQ0i9tAVVKNX+a8IBAJCCrp161aWLl3KoUOHMJvNXHvttVx66aX0798frVZ7WkNXZKZer5dDhw6xZMkSCgoKcLlcXHbZZVx11VVkZWVhNpvPqrZdlmWam5t5+eWX2bNnD/fddx8pKSkEAgH+9re/cfjwYaDdKGNjY1m0aBE6nY7m5mZeeeUVjhw5QjAYxGQyMWLECO666y6MRiMtLS385S9/Eft0nU7HNddcw7XXXotGo6GkpITHH3+c+vp6NBoNOp2O6667jjlz5gCwY8cO3njjDRGsi4qK4sEHHxTCnd27d/Pcc8+JKTqxsbHcc889ZGVl4ff7eeWVV9i5cyehUEh4Il01etW9V/nWSJLEkSNHyMnJYfHixTQ0NDBw4EBmzJjB5MmTcTgc6PV6oTX/JmRZpry8nNzcXJYtW8bevXtJTk5m6tSpXH311cTHxwvN+dm0lAoEAmzYsIFbbrmF5cuXk5WV1Um3HgwGO8lXlQi98m8LBoOdovOKJl/R3vv9/k6GFhYWJh5Iyvkda/E76u6Vayvva7VadDpdp/cDgUCne+t476FQSNz71q1bueeee1i8eLHq3qt894RCIVwuF8XFxaxatYp9+/bR1tbG8OHDufjii+nfvz9xcXFnbFGl7NdLS0tZu3YtW7dupa6ujpSUFB566CEGDRpESkoKDofjjLn606EYd11dHS0tLV9R5JlMJvFQaWtro6ioCIPBgNPpFKtudXU1LpdLKPIUjXxpaSl6vR673U5UVBSSJFFbW0tjYyNWq5WoqCih0y8rK0Or1XZS7ykqO0WRp8QVKisrRZRfUe81NzdTW1uL3W7H4XBgsVhE2rCmpkYUFXUF1ehVzkgoFMLn89HQ0MDJkyf54osv+Pzzz/F4PKSnpzNz5kyGDRtGRETEaWvY5X93uWlqahLFJp988gk1NTXExcVx4403MnHiRGJjY7FYLN/JvcuyjNvt5o033qBXr17C4DZv3szmzZsZOnQoN9xwgwiiPfvssxgMBn7961+LY/Pz81mzZg2ZmZn88pe/BMDr9fLss8+i1+tZuHCh+Lxdu3axatUqMjIyWLBgAdAe63j22WfR6XTcc8894ro7d+7k/fffJzU1lXvvvRdoV/a99NJL+Hw+5s2bJ6TAubm5rF69mtjYWBYuXIgsy9TV1fHPf/6TgoIC2trauvydqO69ytei7CUVQc3OnTt577332LRpExqNhhkzZnDFFVcwaNCg0+bXlWspD45jx47x3nvvsW7dOmpra0VEf+TIkUKS+l2hRO9vuukmXnnlFSZMmCDutampicbGRkwmkwguhkIhocCLjo7GaDSKmICS04+KikKv1xMMBikrK0Oj0RAdHY3JZEKr1eJ2u6mvryc8PByHw4FOpxPVgnq9Xmj3lYdRVVUVTqcTp9MpPJqysjIAIiMjMRqNQixUWVlJVFQUdrtdlAJXVlayefNmHn30UTV6r/LfobiOubm5vPHGGxw5coSUlBTuvPNOpkyZIppVnOkPTBHm7Nmzh3feeYfNmzcTGxvLpEmTmDVrFklJSVgsljNe57v49zQ3N4s0ocViwev1Ul9fT3NzMzqdDqvVSlxcHFqtVij+3G43gUBAPBSUPXjHCbWK8CchIQGz2UxSUhLBYJCqqiqxAms0GpGWA8TDQfmePR4PkZGR2Gw2EhIShDekrMlms5nExERMJlMnd1+ZlttxPPaZUI1eRaDs10tKSvjiiy/Yvn07lZWVpKamMmXKFMaNG0daWho2m+20wTlJkmhtbaWyspK8vDy2bt3KiRMncDqd3HjjjYwbN45+/frhdDq/95ZWyor65ptvUlxczLx584iMjESSJN59910OHjwI/Keg5de//jVarRaPx8PSpUspKioiGAxiMBgYMmQI1113HQaDAa/XywsvvCAaWGi1WmbPns24cePQ6/VUVFTwz3/+k9raWhEEvPrqq7n00ksBOHr0KG+//bZI6TmdTu6++27x3SoNQxSPKzo6mltvvZW0tDSCwSBr165l48aNhEIhSktLaW1t7fJ3ohq9iqg2a2xs5LPPPmPlypVUV1cTHR3NbbfdxqhRo0hMTDxjqszn84kuN9u3b2fp0qUcO3YMWZa59dZbmTx5MqmpqRgMhh90cqvVauXqq69mxIgR4iEjyzJXXnmlmDCraOcV9Ho9kydPZvTo0YRCIfR6PTabDY1GgyzL6PV6brzxRlFwo9VqSU5OFkbqcDi47rrrRAUfQGpqqvjvhIQEfvnLXwpjtVqtwguQZZkePXqI+AEggn3K9ceMGUPPnj2RJIn9+/dTXFzc5e9DNXoVdu/ezSeffMIHH3yA3+9nwoQJ/PrXv+biiy9Gq9WK/50OWZYpLi4WD43S0lJGjRrFAw88wM9+9jORX/8202b+G5Q03IABA+jTpw8ajQaNRoPJZCItLa2TISrHA9hsNvr27dvJZVbO1Wg0mM1msrKyOp3b8X1Fpffl9xXi4uKIjY392vcV3f2X23YrWgedTkdycjJJSUlA+0P7bB6kqtF3QyRJoqamht27d7N48WJKS0vRarX8/Oc/Z8KECaSkpBAREXHGfbYsy9TX13P48GHee+899u7di9/vZ/To0TzyyCP06NGD6OhosUL+GMj/Llb529/+xoMPPig63yxbtozc3FwGDx7Mz3/+c8xmMy0tLSxcuBCj0cg999xDamoqsizzySef8NlnnzFw4EDmzJmD2WzG5XLx8MMPo9fr+c1vfkNcXBySJLFu3To+/vhjevfuzbx587BYLNTV1fHXv/4VrVbLHXfcQY8ePZAkiZycHD766CMSEhK4++67sVgslJeXi+j93LlzGTBgAKFQiDVr1rBu3TqcTie/+93vRLHN66+/zs6dO2lublb39CqdUdpGV1VVcfDgQbZs2cLevXvR6/VcdNFFXH755UJGejo3XpIk0YbqyJEj5ObmkpubK1paTZs2jcGDBxMdHf1f5de/S6xWK9dcc02nlXXMmDGi/FZZ3bVaLfPnz8dgMHTKSAwZMoTU1FRsNps41mg0csstt3xFfHTBBReQkJCA3W4XDzq73c6tt976lS1EVlYW8fHxOJ1OcWxUVBRz585FlmWioqI63W9aWhqRkZHi2NjYWObMmUOPHj0oKirq8vehGv1PGCVVpuTGN27cyMqVKykoKCA1NZXZs2dz6aWXkpqaKkpOv+k6SlfZ1tZW8vPzWb58Odu2bcNsNnPVVVdx2WWX0bdv37MeH/V9o9Fo0Ov1IvevdM5JSkoiNjYWv98v9uUmk4mMjAyCwSAajQa/3y/SbE6nU6jzJEnCZDIxcOBAoYxrbW3FYDB0KslVMBqNwsNQUO7pyy6+cg8d0el0xMTEiP5+HdV+8fHxJCQknJVaUTX6nzAej4eSkhLWr1/Pu+++i8vlYtCgQTzzzDOMHj1aNJQ4k0w2EAhQUVHBli1bePvttykpKSE9PZ3777+fKVOmCFHOma7zY6B06JkzZw4TJkzgkUceITExkZaWFn7729+ydetWAK699lquueYali9fzu7duzGbzUydOpWrrrqKjz/+mDVr1lBeXs6wYcO44oorGD16NBqNhsOHD/PBBx+wa9cuZs+ezZQpU87Y3uu/xe1289JLL7FkyRLR1svtdnd5/Na59yup/Ff4fD6am5spLCwkJyeHvXv30traypgxYxg5ciRZWVkin3w6Nz4QCNDS0kJxcTE5OTns2LGDuro6+vXrx/XXXy9cXqvVes648V+HRqPB4XBw++23M2rUKCIiItBoNBiNRm677TYmTpwIQHp6OqmpqVxyySW8//77aDQaFixYgFarZezYseTn57Ns2TKmTp1K7969xaqamJhIdnY2xcXFjBgx4rQeE7Q/iPfu3cvAgQO/9cPBaDRy1VVXkZ6eTigUoqioiEWLFqkrfXdC2We7XC4qKir48MMPycnJwePxkJmZyQMPPMCAAQNwOp1n3K8rbZ5qampYv349n3zyCQ0NDaSkpPDAAw8wdOhQUVN+PqAY+IgRI8jOzhbTb7xeL4mJifTo0UM0lgyFQgwcOJCePXtSVFREZWUlGo2G2NhYZs2axT/+8Q8qKio6rahKP70JEyYQEREh1HpK48uOmY+2tjZKSkp4++23+f3vf9/J6JUtlJIe7JjlUD5P6QIUFhZGRkYGvXr1wu12YzAYhHKvK6hG/xOgtbWVTZs2sWLFCjZt2oTZbObqq6/myiuvJCsrq8t/DD6fj4KCAlauXMlnn32G2+3m6quvZubMmYwePfqcXtG/CaUBxb/+9S8iIiIYNGgQAB9//DHbt29n8ODBzJ49Wxi+w+FgxIgRHDhwgG3btjF16lQcDgfJycmMHj2agoICKisrxWBMl8tFYWEhd9xxB2azmUAgQFVVFbW1tURFRYlWXABHjhzhb3/7m+iPpzwYoH0bUldXR1NTEykpKVgsFvG7+f1+GhoaiIqKorq6WrTXrqys5PXXX6egoEB177sDkiRRWlrK5s2beffdd6muriYhIYE//vGPjB07FqfTSXh4+BkNXv739JRdu3bx5ptvcuzYMSIjI1mwYAFTp04lIiLijAq8cxlF/jpnzhx69eolXp86dSrjx4/HaDR+pbhn6tSprF69mh07dojmFEr2o6SkhJ07dzJ06FCgfVKO0ju/oaGBFStWcOzYMcaPH89LL72Ew+HgV7/6FQ6Hg02bNnH06FHcbjevvvoqkyZNYsKECdTU1JCXl4der+fQoUNs3ryZX/ziF0ybNo3S0lKeeeYZysrKmDNnDs8//zxZWVn8/ve/Jz4+ngULFjBgwACOHDnSZQ3E+flLdlNCoRBNTU2cOHGCXbt2kZuby8mTJ0lKSuKyyy5jwoQJJCcni8aQ34Si3S4tLWXPnj3k5uZy6NAhYmNjufbaa5k4cSK9evXqlDI6n+lYOKTX6zEYDCL95nK5aGtr6ySmSUtLY8yYMSxevJijR48yYMAAWlpakCQJSZLYunUrs2bNwmw2c+TIEYYNG4Zer6ewsJD8/HxuuOEGsrKyCAQCPP/88+Tk5DB9+nSmTp1KTk6OaGfdu3dvfD4f77//PsnJyfTr14+0tDS++OILFi1aRGpqKikpKYRCIU6ePElVVRUXXnihkBYrRq6oBLuKavTnOEqqzOv1UldXJ3q7Hzx4kLFjx3LfffcxdOjQM8pklTSP1+vF7XazZs0aPvjgA/bt28eAAQO45ZZbGD16NKmpqeelG/9NKFVyzz33HCNGjGDevHkkJiYSCAR46qmnREXbxRdfzI033gi0q/EmTpzI4sWLWb58ObfddhuHDh1i2rRpYiU/dOgQPXv2xOv1kpaWBrQ3ycjKyqJnz54i9abVasfbGyIAACAASURBVCkqKmL69Omib57b7SY6Ohqr1crRo0dZvnw5V199tajq69GjB/n5+Rw+fJihQ4eK4qahQ4eSmZmJz+fjrbfe4tixY6KC72w656hGf47jdrvZv38/H330EcuXL8fpdDJu3DgefvhhBgwYIPqsn0kXr7ShWrNmDe+++y46nY4RI0bwj3/8g+zsbMLDw7t0nfMNjUaDxWJh2rRponxXo9FgMBiYO3cuR48eBRCGC+059F69epGdnc3atWuZMGEChYWFXHvttbS1tbFmzRo2btwo2lilpKSg1WoZMWIEF1xwAeXl5axevZqDBw/icrm+sX+d3+/n6NGj+P1+YmNjhax2zpw5/OIXvyAuLk48gC0WC7169RI9+ubOnUthYaHQ3h8/frzL34lq9OcgHo+H+vp68vLy+PTTTzlx4gRGo5H58+czYsQI+vTpQ3R0tBix/E14vV6amprYvXs3H3/8MUeOHAFg1qxZjBkzhvT0dOLi4jAajT85Y++IXq8nNTWVtLQ0EVRrbGxEr9fTr18/0XVWQaPREBMTw7hx43jppZdYu3Yt4eHh9OzZk+nTp7NhwwY2bNiA0WgU/QSUgOHGjRtxu90MGTKE9PR0oQP4OiRJoqmpCa/XS0REhBipBe0eiqLjV+5JyQbodDri4+Ox2WzU1tZSV1eninPORwKBAG1tbdTW1nLs2DE++OAD9u7di9FoZOzYscycOZPevXtjsVhOa6BKfXddXR0lJSV8/PHH5OXlodVqyc7OZtasWfTr1++8Ds6dDYoxvvnmmwwcOFCo2jZs2MDatWsZM2aMKJftiM1mY+zYsbzwwgts3LiR2267DaPRSEZGBoMGDWL16tXY7XYuvfRS9Ho9oVCInJwcPv74YxYsWEBmZiYlJSVfm9pUKuW0Wi1OpxOXy8WJEycYPXo0NptNtBBvaWnp5IEoKA+AUCjEG2+8wfbt2/H5fKp7fz7QsTtNVVUV69atY/Xq1ezZs4f09HTmzp0rylHPFJlVgkz19fVs2LBByG2V4Ny0adPo06dPtzD0L2MwGBg4cGCn7zA6Oprs7GwSExO/9hylMi8hIaHTvt3pdDJq1ChWrlwp9ujQ/v0rI6YdDgehUEg0yejY5EKj0Yhhm6FQiD59+gCwfPlyUlJSGD9+PF6vl7Vr1xIbGyvuT4ntdDRsnU7HoEGDcLvdHDt2rMvfR/f7CziHUGSyH374IStXrsTj8TB48GBeffVVMjMzsVqtmM3mMxq80nt93bp1LFmyhMbGRvr378/TTz/NyJEjxXV+yi78N6HRaLBarUyZMqWTgY8aNYphw4Z1GnX1defdeOONHDp0SMya1+v1DBgwgOzsbG644Qaxx9ZoNIwePZrXX3+dRx55hIyMDE6dOkVzczO7d+/mtddeY8aMGcTGxrJ582befPNNevbsyezZs1m4cCHPP/88CxYswGazERERweWXX86UKVNoamqitraWlpYWDh8+3Klq0W6387Of/Qy73c7atWtV9/5cRFnVa2pqKCwsJDc3l927d9Pa2sro0aMZOXIkw4cPJzY29rSFK4qHUFtbS1FREbm5uezcuZPGxkYGDx7M8OHDxTz371sHfj7g8XhYu3YtdXV1jB07Vijn1q1bR319PdAuwx09erTwhJRe9orsNioqimAwiE6no0+fPtx0000MHToUrVYrXOsZM2aIrjmpqalMmzaN3bt309jYyNSpU4mKiuKKK65Ar9cTHx/PuHHjxGfY7Xb27t1LKBQiIyOD8ePHY7VaKSsr4+KLL2bkyJEYDAYkScLn87Fx40aqqqqQZZlDhw6J/vtdQTX67xlFXun1emltbaW6upo333yTrVu34na7ueSSS7juuutEcO50KNdpa2ujoaGBt956iw0bNtDQ0MDYsWO58847RQtqlXYUQ9Dr9ZjNZrEaBoNBkpKSxLAJRQOh/AZKi26dTkffvn1FW6uIiAhiYmKYNWsWtbW1YkS00vhi/vz5BINB9Hq96PIrSRJhYWFYLBbGjRvHiBEjAKiurqaqqgpo9zxmzJiBRqMhLCxMlC+HhYUxYcIEDAYD8fHx6PV63G438fHx1NXVIUnSWUui1W643zOSJNHY2MimTZtYtWoVH330ERdccAGTJ09m+vTpYp99pu40SkBq69atrFq1ihUrVtCvXz8uueQSZsyYQf/+/UU0/4fuTnOu0nHYxcqVKxk8eLAYqaU8jDsOm/i6KTxfNo+O73/Te8pD4HTnft35Z3P9jve+efNm7rrrLnXYxY9NS0sL1dXVrFu3jo8++ojm5mZSUlJ4/vnnyczMJCkpScxhP91erLW1ldraWjZs2MCqVatoaGggLi6OJ554giFDhpCcnIzdbj+rgovuhBLc/OMf/8j//u//csEFFwDwyiuvkJOTw/Dhw5k/fz42m426ujoWLFiA1Wrl//2//8eAAQMAePfdd1m1ahVZWVnccccdOBwOGhsbuf322zGbzTz00EP06dMHSZL44IMPePvtt8nKyuLOO+/E6XTS0NDAvffei8Vi4b777qN///6EQiE+++wzXn31VUaOHMn8+fNxOBzU19fz0EMPodFouOOOO+jfv7/osvPiiy8yYcIEbr75Zmw2G/X19Tz++OPk5+fT0tKiuvc/Bora7dSpU+zZs4d169ZRVVVFVFQUN9xwAxMnThSNIU+3Gvt8PtxuN2VlZezdu5f169dz6tQpnE6n6Kjas2fPn3x+/btCq9WK3vQKMTExxMXFdepEo9Fo6NmzJzqdrlOXXofDQXx8PDExMZ2OTU1N/cpvEB4eTkJCAgkJCeJYvV5PYmIiFoulk9rRbrd/5Vhl3r3S20953el0fuVYg8Eg5tUrysKuoLr3/yVKOiYQCFBSUsLKlStZu3YtFRUVjB49mquvvpoLL7wQp9N5WkNXrqMMUVi1ahWffvopJSUlDB06lNmzZ3PRRReJwQwqZ6aje//ee+8xZMiQTrPolN8N/jOrTjF25beQJEm468qsOeX8jrlxZS/+5Vl2HWfhfXmWXcdZdzqd7iuz7JSOPsr7XzfLTpZltm7dyr333qu69z8UjY2NHDx4kPfee4/169fjcDgYN24cs2fPpnfv3phMJjH95HQ0NzdTVFTE+++/z5o1a7BarYwaNYpHH32Uvn37YjabuzyaWeU/KKq3//u//+Oiiy5i1qxZRERE0Nrayocffkhubi7Q7g0MHDiQefPmodPpqK2tZfXq1Rw+fJhAIIDJZCIrK0ukyFwuF0888YQI8Ol0Oq699louuOACDAYDpaWlLF26lIqKCqB9tb/mmmsYO3YsAPv27WP16tU0NDQA7d1xf/7zn9OnTx9kWaagoIClS5eKh0Z8fDxz5swhMTERj8fD5s2bWb9+vZhnr4zU7gqq0Z8lsizj9Xqprq4mNzeXbdu2cfjwYcLDw/nlL3/JsGHD6N+/P5GRkafdr8uyjM/no7q6mry8PLZt20ZRUREmk4kbbriBYcOGiXnuZ+rGovLNKDr7/v3706NHDxHIMxgMREREMGzYMHFcx669ZrOZHj16iL56er2epKQk8ZuGhYUxaNAgsRorbbHDwsLQarVYLBbS09OFNkCr1XaS+oaHh5OZmSkm4FitVpGm1Wg0REVFMXToUOFJ2Gw2cW2lSjA7OxtJkigqKmLHjh1djumo7n0XUNyplpYWXC4Xhw4d4q233uLgwYOYzWamT5/O9OnTRXDudIYuSZK4zpEjR3jrrbfYv38/YWFhXHbZZcycOVNMa1X571Bm2d1yyy0sXbqU7Oxs4b63traKcVWKtFnpN6e4+crDtq2tDb/f3+nYUCgkjjUYDGI+ndfrxev1EhYWJkZoKb+58rD5umOVHoPKdCBAdMSRZRm/34/H48FgMIix3Uq58ObNm/n1r3/NO++8o7r33xWKoGb16tWsWLGCAwcOMHz4cO6++24uvfRSEhMTOxVHfBNKJFlJue3Zs4ehQ4eyYMECpkyZQkpKSpeuo9J1lHz76tWriYmJEcq6TZs2UVhYSJ8+fZg8eTJWqxW3280//vEPLBYLP/vZz+jVqxeyLJOfn09BQQE9evRg6tSphIeH43a7ee211zAYDMyYMYPU1FQkSWLXrl1s27aNlJQUpk2bhs1mE9p/rVbL1KlT6dOnD8FgkL1797Jp0yYSEhK44oorsNvtNDY2snz5cgKBABMnTqRv376EQiF2797Nxo0bSU5OFluMuro6UVvR1tamRu//W0KhEG1tbZw8eZLly5fz0UcfYTQaycrK4oEHHiAjI4OIiAgsFstp99nKdUpKSlixYgWrVq0S1Vn33nsv/fr1E/XS6n79+0OSpE4qR2WibMcuvgaDAYfDQTAY7ORqK6u7cqzSd0+J3CuddxS3XpHwhoWFiWk6yjnKdXU6nfAKlem0yhZAOVaZTqvRaITcV5mmq3yGTqcT6kHVvf8WyLKMx+OhoaGBQ4cOkZeXR15eHsFgUAxxHD58uBg3fDqU2XAdr+P3+0lOTmbq1KmMGDGC2NhYNb/+PdJxVPXLL7/MqFGjiI6OFh1zXC4XHo+H8PBwYaCAKGHVaDQifRoIBMSoapPJJOodZFnGZDJhNpux2WwEg0HRoUeZcitJEm63W8yjM5lMeDweGhsbaWxsxGKxYLPZsFqtmEwmUW6rNMGE/2wN7XY7YWFhSJKEy+WiubmZvLw8/vznP7NkyRIGDRqkuvddRUnB7N69myVLllBQUEBzczNXXnklV1xxBVlZWWeMwgeDQQKBAD6fjwMHDrBs2TLy8/NpamoS+35lX6mu6j8MsizT1tbGp59+SktLCzNmzMBisWA0Gtm7dy+7du0C2g29X79+XHnllWi1Wpqbm1m3bh1HjhwRU2sHDhzIJZdcArR7cB988IEIxGm1Wq688koyMjIwm81iG1ddXQ0gYjZKQ82Kigo++ugjXC4X0C7vveaaazCbzURERLB//34+/PBDEb2Pjo5m1qxZWCwWAoEAu3fvZsOGDUiSxPHjx/F4PF3+TlSj/zctLS2sWrWKZ599lpiYGGbPns1VV10l3KmOK8E3oYxmXrJkCfv27SMtLY1rrrmGmTNnEhMT0+XrqHy3hEIhKisrKSsro7W1FYvFQigU4vDhw5SUlAB85SHs9/spLS2lpKREGL2ykiuZl+PHj+Pz+cT5ZWVl9OrVi7CwMFpaWjh58iQ1NTVA+0OlvLxcKALr6+tFFR5AU1OTmHAryzINDQ2duuEonqMyaefkyZOcOnVKlGUrD4euoLr3/8bn81FSUsK+ffvo3bs3qampQlBzumi82+2mvLycTz/9lPz8fKqrq0lNTWX8+PEMHjyYtLQ0sX9Ujf2HRXHvb775Zv71r38xbNgw0TxEGUXldrtF8NRoNAqFns/no62tDa/XiyRJ4n2Hw0FYWBiBQIDa2lpCoZAQ9ihyaK1Wi9/vp6WlRaT0lPHVStVjS0sLbW1t+Hw+EdW3WCyEh4d3yvB0VOrZbDaMRiOhUEioP0OhEPn5+SxcuJAlS5ao0fuzwWg0kp6eLqK7pzN0v99Pc3Mz1dXVFBQUsGrVKqqqqoiLi2Pu3LlMmDCBuLg4EcBR+XFRYjVhYWFij1xXV0djYyN2u11Ur/n9fg4fPoxOpyMpKYnIyEgAampqqKurw2azdUqlulwuMZfeYrGIKb41NTXYbDZx3UAgwIkTJ2hra0Oj0RAeHo7FYsHn8+FyuUQzjrCwsE6xAqUlllK0dezYMcLDw0lMTBQ9DcvLy8+qKSaoRt+J0xmoUsPu9/uFcu6TTz7B5XIxYcIEbrvtNsaMGXPG9tMqPyxKPrygoID+/fuLlXb//v2io+0ll1yCXq8XTS+VOXY9e/ZElmWKiorYvXs3qampTJo0Cb1eT2trK+vWrcNgMDBt2jSRsisuLiYvL4+UlBQmTZqEzWajpaWFnJwctFotl1xyCb179yYYDHL06FG2bdtGfHy8qKlvbm5m8+bNBAIBLrroIjIyMggEAhQVFZGXl0dMTIxI2dXX17N161by8/Pxer1dNnzVve8CgUAAl8vFvn37eOONN8jLyyMiIoLJkydz1VVXkZiYiNVqFaIJlXODjuKcZcuWMXToUCHOaWtrE+IcpatQMBgUNfSKMAbam3AoE2wVwY0i1lLEOYqIxuv1imOVlJ4kSSLgp4h2lLiAz+c77bEdxTmKkKejOMfr9bJ582buv/9+VZzz36Lk16uqqigoKCA3N5cjR45gt9u5/vrrGT9+PP379xf7OJVzE0Wcs3TpUsrLy5kyZYqYSZ+Xl8fu3buBdm187969mT59OlqtlqamJtauXcvRo0cJBAJi+zd+/HjCw8Npa2vjrbfeEqIYRXijjOuur69n+fLlVFVViT37xIkTRSCvuLiYjRs30tjYCLRH76dOnUpqairh4eHs37+fzz77TAToYmJiuOKKK7DZbAQCAXbt2sWWLVsIhUKcOHFCLa39LvD5fGzYsIG33nqLo0ePotVqmTdvHpdccglpaWmqHv48QQm2vvPOO9TV1TFu3DjCw8OFF/D2228D7TGdiRMncsUVVwCIgSDr1q3D6/WKPntKz8HW1lYWLVokutcobbZ79eqFRqOhvr6ed955h8LCQiHwiYuLE0Z/6tQpFi1aJEpik5KSGDZsGKmpqQAUFRXx0ksv4ff7kWVZtPNyOp34/X527NjB3//+dwKBAB6PR1QDdgXVvf8GampqWLhwIQCXXnop06ZNw2QyifJGNUB37vN1pbVKylSW5U7lq0rprOK1KaWxSopOeV8peulYWqu8bzAYRGmt4pIr0f1vKq1VVnKldFZ5PxAIdOp+q2w5OpbWKg+EL774gnvuuUd17/9bHA4Hv/nNb7BYLERERAiXUOX8QhnjXVBQQFpaGvHx8QDs2bOHEydOkJyczAUXXIDJZMLlcrFmzRqMRiNDhgwhPj6esLAwCgsLOXLkCMnJyWRmZmI2m/F4PKxbtw6LxcIFF1xAfHw8kiRx+PBhDhw4QI8ePejXrx9WqxWv18u6deswmUxkZmYKgU5ZWRm7du2iT58+pKenYzAYaGtrY9OmTWi1WjIzM4mPjycUClFWVkZ+fj79+vWjV69eWK1WgsEgeXl55ObmigdAV1D/ir8Bo9FI//79SUtLExpolfMTZQS3UrsO7WOjt2zZwsGDBzvVoefk5LBx40a8Xq947eTJk2zZsoW9e/cKwwoEAmzatImcnJxOxnbq1Cm2bNlCXl6eeK21tZXNmzeTk5Pzletu3bqVzz//XLzmcrnYtm0bOTk5Yr8PcPjwYbZs2cLq1avFa83NzWzfvp0dO3YIkVBXOGv33u/34/P5sFqtqiF8DYrrFQgE0Ov1P6lhkOcbHd37FStWkJWV9ZXGmB2VbFqtVrjXHQdUAMJF73j+l2fUddTsf/l85f2O8+g77sMVgU/H9zveW8exVl++9y1btny/jTGXLVvG008/zaZNm8RoX5X/4PP52LlzJy+99BJ33XUXo0aN+rFvqVvTsaZCr9fTo0cPHA4HHo+HEydOUFlZKY612WwMHz5cRO+Li4tpbW0VLaydTid9+vTBYrHQ1tbGzp07RUxAq9WSlpZGQkICBoNBiGkUaS1A79696dmzJ9DuEVRUVAjNvNVqJS0tjcTERGRZpry8XMweBMQsvaioKLxeLyUlJVRXVyNJEoWFhd/vWCulO2swGDzbU7sFkiTh9/tFBZfKj4tGo8Hv93PgwAHMZrMYT6XT6Thw4AAnT54Ux0VHR4ue9FqtlmPHjlFRUUEoFEKv19OnTx8yMjJEEHffvn2dUnYmk4nk5GTxmXv27BHaeq1WKwwX2u1o586dnYy+R48e4l5cLhd79uwRq7nSRFOj0aDX6zl+/DhFRUVCEKT0+usKaiBP5SeP1WplxowZQnuvGO2UKVPw+XwiIq/T6fB6vWi1WsxmMzNnzhQCGkmSMJlMYrtmNBqZPXu2MHhlmAW0e3tRUVFcf/31wsUPBAKYzWZCoRA6nY6MjAySk5Npa2sToh9FiOPz+UhNTeXmm2/+ytRaxeuYMmUK48aNw+fzkZuby5YtW7qcUVI35So/eQKBACdPnhTpM2h3r3fv3k1dXR3h4eE4HA70ej35+fns2LEDj8eDyWQSTTALCwspLy8XK28oFOLAgQMcO3ZMNN8ICwujsrKSbdu2cfLkSYxGI06nE6vVysGDBzl48KBw9/V6PS0tLRw4cICmpiaMRiMGg4FAIMCOHTsoLCxEq9XicDiw2+20tbXxxRdfUFJSIurszWYzJ06c4NixY+e39v7YsWNC1HA6wYGSGz3Tax1RAjX/8z//Q1pamppr7wYoirz333+fkSNHig40SjfZUaNG0aNHDwwGA36/nxdffBGTycSf/vQnUUexc+dOVq5cSXZ2NrfffrtIrb366qsYjUYee+wxHA4HkiSxZ88ekS+/7777MBgMuN1uFi1ahF6vZ+HChdjtdiRJYt++fbz++uv06tWL3//+94SFhdHY2MjixYvxeDzcc889DB48GEmS2L17N//617/o2bMnf/jDH9Dr9dTV1YmeDa2treevIq+xsZGCggKqq6uJiYkRk2IGDx6M3+8XwojKykocDgcRERHU19cLNywtLU10Lqmurqa1tZWePXtiMBgoKyvjxIkTNDc3n/EBofLTQKPR4HQ6ufvuu0lKShKvX3bZZYwfP76Tyx4WFsajjz4qVm6FCRMmkJ2dLcRZ0N4t99FHHxUz8hTGjh3LgAEDsFqt4li73c6f//xntFqtKPjRaDSMGjWK9PT0TsdGRESwcOFCJEkSWxFlIm56erooDYb2xhr3338/W7Zs4U9/+lOXv5NzzugVF+ySSy5h0qRJVFdXs3LlSv7yl7/gdrtFscOHH35IZmYm2dnZ5OXl0drayvHjx7nxxhspKyvD4XCQk5NDcXExN954IzExMbz55ps888wzZ9VwQOX8RtkLR0REdNpTx8XFidSqoo5T9tqAKGaRZRmbzSa0Goqiz2AwiEg7tBfwhIWFERkZSVRUlJgnrwTq4uLiOhVkSZKExWIRcm5lMTMYDKSmpgq1oJLXt1gs9OrVS/TEU2IFUVFRREdHi959XeGcM3qgU+BDaf6nSCCVFsDKj6fUSNvtdvGeEuwwmUwiUNJRIqnSfZAkiYaGBh577DGys7O56aabSElJwev18vjjj4vOOUrzyaeeegqtVkt1dTV///vfRVcag8HAoEGD+OUvf0l4eDhNTU08+OCD4sGg1Wq5+OKLueqqqzAajRw9epSXX35ZRO81Gg1XXHEFM2fOBGD9+vV89NFHot213W7nrrvuIiMjQ0hrX3/9dfFQcTqdXH/99QwZMgSv18uLL77IkSNHCIVClJeX09TUdP669x1RGhMo3UIA8bT1+/2i6YDSGVQRCykpFqPRKCaQwNdPCVX5aaPRaHA4HNx+++0MHToUp9MpdPD33nuvUL0pwyo6zo674447RP5bKcFVGpmGh4ezcOHCTmOxlAEnOp2OtLQ0fvvb34qVWhlgoTBmzBgyMzNFnt9kMnVy/bOysvjDH/4g/maNRiMRERGilPfWW28Vhr5jxw4x9LIrnLNGr/wISrfRL2uLleEDyv8rP5gS/FNqkV0uV5fH/aj8NFE8R2XEGLTPhne5XFitVhITEwkLC8Pr9VJYWCiGSCoxgMrKSiHhVYJ7SoBQr9cTFxeHw+FAlmVqa2s7dc5RIvLHjx+nurq6U9sspQOT3W4nKioKo9GI3+/n5MmTaDQaYmNjsdlsyLIsxD6RkZHExMQQERGB1WqlrKwMj8dzVvGpczZlp5QjKkbf0tLSyXiV5gOKJLhjq2D4z3SQ5ubmTrO8VboXkiRRV1fHI488QmFhoXj9rbfeYu7cuTz//PPCG6yvr+emm25i/vz5HD58GGj/e1q+fDlz587lmWeeEUHgxsZGbr75Zm6//XaOHTsmPuujjz5izpw5PP300zQ2Nopjb7nlFu68804OHjwoJLzr16/nuuuuE8eGQiEx1vqee+5h//79opouJyeH2bNn88ILL9DU1EQoFKK6uprf/e53/OlPf8Ltdp//s+y+vNK7XC6io6OB/5QtKv3HlBSIoomWZVns75ubmzuVMKp0L7RaLTExMTz55JMMHjxYvD5//nx+8YtfiC630B4NX7FiBXq9vtOwizlz5oi9usPhEK768uXL0el04litVsvMmTO59NJLMZvN2O12ceyyZcvEMAsldXz55ZczduxYMcdOp9MRHR3NokWLxGw9vV6PTqdj2rRpjBw5ErvdLuJcCQkJ/P3vf2fLli08+OCDXa6FOWeNHhDDAhU3XWlUCP9Z6YPBIBEREeJpraz0StBPkiS8Xq8qG+6mKAvEgQMHCA8PZ9CgQSJAXFFRIVZprVZLQkIC2dnZaLVa3G43BQUFIpAXFhYmGlJCez38gQMHxJ5fq9UyZMgQ4uLisNlsNDc3k5ubS2NjoyimUUpwoX3LcOjQISHWsdvtDBo0iJiYGBISEigpKSE/P1+s3g6HgyFDhojOOcXFxUKGe+TIkbMqrT1njV75ohSJ4pdH8XYsMFAKKIBO8771ej0Wi0UYvRrI637IsozL5eKVV17h0KFDPPjggyQnJxMIBHjuuefYt28f0P730qtXL9544w2gvWz1rbfeYteuXSKTNGbMGB544AFMJhNut5snnnhCRN91Oh233nors2fPRqPRUFpayt/+9jdR0BMWFsZNN93EvHnzgHbd/gsvvEBdXR3Q3g7rscceIyYmBlmW2b17N48//rj4e05KSuKhhx4Sk3KXLVvGmjVrCAaDNDU1nVVH3HPW6BWU1JsyCQT+8/SWJEn0G6+trRV7JUAUJkRERODxeAgGg6oYpxui5ORfe+01hgwZIvLZVquVF198sVOhSsfS18TERJ588kmxLVQWISVPHx0dzccff9zJ0DqmhTMzM1myZEmnhapjAL7tjwAAChhJREFUyeull17KxRdfLN7vWNar0Wi4/PLLmTx5sjheidormYPf/e533H///QBs3bqVe++996fh3gNipW9paRFfWigUEkUQSvpFMWgleALtP6LT6RRpE6WgQaX7oCwE9fX1tLS0iC1iZWUlLS0tmM1mEWVva2vj0KFDQjMfGRmJLMtUV1fT3NyMxWIRk4qUCTh6vR6HwyEEObW1tTQ2Noq5d2azGb/fT1lZmUgfKgM1WlpahPY/IiICg8GAz+ejoqICWZax2+1EREQgSRLNzc3U1tZit9txOBxivFVtba2oej2vO+cohqzk281mM4FAAIPBIAJ1Hf+RHSuR6uvrRUBPUWIp8t2OckmV7oHSGPO1114TI6YANm7cyJNPPsknn3wivMNgMMjTTz/NU0891cmz3L59O08++SQrV64Ux3q9Xp566imefvppkWsH2LFjB0888QTvvvuu8BJcLhdPPfUUzzzzDE1NTeK+duzYweOPP85rr70mVvyGhgaef/55nn76acrLy8Wx27dv569//SvPP/+8SEvX19fz0ksvsWjRItE2uyuckyu9MvK3Y69xpQ2x0ixQ6fv95c4jjY2NpKamip7mkZGRoouN1WpVV/puhhIFv+GGGzpp7ydNmkRWVhY2m014kCaTiQceeABZlkWmSKPRMGbMGKF77yjO+dWvfiW2l9D+dztixAhSUlKIiIgQx0ZGRnL33XeLnL6y9Rw5ciQJCQlER0eL4ahxcXHMnz8frVZLUlISWq0WrVbLhRdeSFJSEnFxcaJPf2JiIvPmzeP/t3d3IU39fxzA386mtjndUmeGtqZWRBdJRIJBkPaAlDdRu+hJIXU10aQIpOgmSs0eIL1IAs2YRhc90UUhoaHRRUVE3fXgQ1FTLIdbbsez4zn7Xfg/h9afXz9XWzvb+bwgyDi6r9p73+18v9/PZ/ny5WhpaYnuzTni0oZ4h14MvbjRAYBUClh8hhQ35Ljdbuh0OrAsC5VKBYPBENDUIJhSwST6iQEzmUzSeXdgbnlOfJktvg9Xq9XIzc0FENjQMi0tDQaDIeDa+Ph45OfnS38XGQwGaZ+++O8qlUpql/bjtSkpKVi1apVUBku8Ni8vT7pWDLJOp8Pq1asDro2Pj4fZbManT5+CKl33W6EXu3uEYy87wzDSnw8fPkg7p5xOJ8bGxqT3QGJJIYZhsGjRIoyOjkp9vVesWAGXy4WpqSlwHAeHw4GxsTHpJZvX6w1oDhhKMzMz8Hg8tC9AJvz/a1Xd1dWFzMzMiDy+eEDmx8CGktj7br6CDr14wOXBgwcBz5yhMjIyAqfTievXr+PevXsA5pbnpqam8Pr1a6m6ycTEBF68eIHk5GSkpKSA4zi4XC6wLIvBwUGoVCpwHCft5Ovr6wPHcdBoNBgYGMDw8HBYQu/z+TAyMhJQw5xEhliiymg0or+/PyJjEE/rOZ1OqSBGqKlUKuTk5EhvEf5L0NVw+/r60NHRIRXlCzXxmfHn8+7ixz/uunO73fD5fEhLS5O+2Z+v+5kgCH+lbXRBQQHKy8tRUFAQ1schvyY2rYgUhmHw9OlTNDQ0oKmpCVu2bAn5Y4j/l+d7vDboqWjdunUwmUyy2OzS09ODly9f4uTJk9Dr9bI6OqvVagN2EJLIENe3I2V2djagBl8kxyIKOvSpqakBVUUiSa/XY+HChcjLy0NGRga9nCZkHmS5Tk8ICR8KPSEKQ6EnRGEo9IQoDIWeEIWh0BOiMBR6QhSGQk+IwlDoCVGYqN7CFhcXB57nwTCM1MmGEDlhGEbqgiMXUZ0StVoNr9eLhw8fQqfTheXYohL4/X6pN0C4jn8qlc/nw/DwsKxOXcpjFL8pPT0dycnJsNvtkR5KVBJnn5mZGXz58gWzs7PIyMhASkpKUA0Rya8lJCQgNzcXWq020kMB8BtHa+VkenpaqnRLgicIAliWRVNTE3p7e5GZmYnx8XE0NzejqKhIagFF/oxY81Gr1criZxrVM31ycrLUfIAER2yLZLfb8ebNG1gsFpSVlcFut+PGjRtQq9XYsWMHEhMTZXVkmfy5qA49+T2CIGBychLd3d24cuUK9u3bB5vNhqVLl8JsNqOlpQXnz59HUlISNm7cCJ1OR8GPIXTHRmHEmnHt7e24evUq9uzZgyNHjmDZsmVYsGABsrOz0dDQgNLSUhw8eBB37tyRWi+R2EAzvYLwPA+Xy4Xm5mY8fvwYu3btQl1dXUC5MZVKBaPRiKqqKhgMBnR0dGBychIVFRUB15HoRaFXCJ7nMT4+jps3b6K3txfFxcWoqqpCVlbW/92lT0hIQFZWFioqKsAwDO7fvw+e57F//36kp6cjMTExQt8FCQUKvQL4/X5MTU2hs7MT7e3tKC8vh9Vqhclk+tfPEfsA1tbWwmg0oq2tDR6PB1arFYsXL5bNmjMJHv3mYpzYqvvy5cu4e/cuLBYLampqYDQa5/X5Wq0Wu3fvhl6vx+nTp+F2u2Gz2bBy5cowj5yES1Sv05Nf43keExMTaGtrQ39/P0pKSlBdXY0lS5ZArVbP++sIgoDv37+jt7cX3d3dyMnJweHDh5Gfny+LdWcSHLorE6MEQcC3b9/Q09ODnp4ebNiwAZWVlTCZTEEFHoDUr23nzp2oqqrCu3fv0NjYiKGhoaAaJxJ5oJk+Bvn9fng8Hly4cAGdnZ3Yu3cvampqkJ2d/cdfm+d5PHnyBKdOnUJWVhaOHTuGwsLCEIya/C0U+hgjCAKmp6dx5swZPHr0CNu2bUNdXR3S09ND0mhBXOd/+/Ytzp49C5ZlUV9fj02bNtEGnihBoY8hPM9jbGwMdrsdt27dQnFxMWw2G0wmU8jX1zmOw/Pnz9HR0QGXy4VDhw6hsLAwLL3aSGjRe/oY4ff74XQ60dXVhdbWVpSWlqK2thZmszksG2rUajWKiopQX18PvV6PEydOYGBgAB6PJ+SPRUKLZvoYIAgCGIbBuXPncPv2bZSWluLo0aMwGo1hX0/3+Xz4/PkzGhsb8f79e1itVlgsFlrHlzEKfZTjeR5fv37FpUuXMDg4iK1bt6K6uhpGo/GvNUtkWRYOhwOdnZ149uwZtm/fjgMHDiA1NZW27coQPR1HMUEQMDExAbvdjmvXrqGkpATFxcWYnZ2Fw+H4q2OJi4vD5s2b8fHjR7S2tkKj0aCsrAwZGRl0g09maKaPYl6vFxcvXkRbWxs4jsP69esj3h7b7Xbj1atX4DgOx48fh9VqlU2XYzKHZvooNjo6Co1Gg8rKSgiCIIuCFzzPY82aNWBZFoIgYGhoCGvXro3omEggmumjmMfjAcuy4HleVtVWgbnVBJVKhaSkJOh0ukgPh/yAQk+IwtCtVUIUhkJPiMJQ6AlRGAo9IQpDoSdEYSj0hCgMhZ4QhaHQE6IwFHpCFIZCT4jCUOgJURgKPSEKQ6EnRGEo9IQoDIWeEIWh0BOiMP8AC0WP2XCKYS4AAAAASUVORK5CYII=)
- Water overflows and the right side of the balance tips down.
- Water overflows and the left side of the balance tips down.
- Water overflows but the balance remains balanced.
- Water overflows but which side of the balance tips down depends on whether the brass weight is partly or completely submerged.
The correct answer is: Water overflows but which side of the balance tips down depends on whether the brass weight is partly or completely submerged.
Related Questions to study
physics-
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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2aNaAoClOmTMHAgQMZTAxqtRrbt2/HuXPnoFKpsGTJEoZ12263o7y8HG+99RYA4LHHHsOQIUPctj/ciS5TQqFQCJFIBKVSCblcTrT88Xg8iEQiqFQqF40FqZ9QKIRMJoNSqYS3tzfxZaC5SWljkEgkInKNcjgcl+VTIBAQlYHD4biSk4VCIcRiMSs3qre3N3x9fSGTyVjpNkQiEby8vKBSqVyUjyRIpVLXWPczIVokEkEkEoGiKNa0KLpdKpUyCvncCT6fD5FIBD6fzyoz/SwkEkmbHLMCgQASiYRBh9K6j9PphEQigUgkYpVLKBRCKpWCx+OBx+MR55yiKJeBhf4NrUHzF9G/jeZEuhe4RfTUGt9++y22bduGmTNnYuLEicQ+v/zyCz755BMMGzYMTz75JCwWC3g8Hnx8fBgTRue50cVevLy8iIpIUx5arVbw+XzIZDLGRNDkUXSWgZeXFwQCAWMsjUaDBQsWAACWL1+O6OhoxuQ7nU5YrVZotVo4nU5IpVLWB97U1ASr1QqKoiAWi13cO3eC5kW12+0Qi8WQSCTEsXQ6Hcxms4s/h34RHQ4H5s+fD5vNhj/96U9uO+0NBgMOHTqE2bNnIy8vDwqFwpUHx2Zgs1gs0Ol0sFgsEIvF8Pb2Jsqs1WphMBhcLyppIaJ/v9lshkAgYOxi7pRTq9WCy+VCKpUS5aJ5aul5UiqVRLnMZjMaGhpc7xVpUbbb7dDpdDAajS6LbOtAEJpsjK5lQo/F4/Fw7tw5rFq1CvHx8Vi5ciXxN5HQZV9CiqLu+smmzf13I2WiKOquZa05HE6bK2jr8SiKYjUv01/C9pjx27MtuZMYqy3IZLIuyUxpz33aUpY70R4XRHt/f3ss7nw+n9UneSfa467g8XiQy+Vtvls02VhH3DNs8KRUe/BfB6fTCZ1Oh/r6emg0GlgsFtjtdlAUBafT6fID0zVQfuvMAL9t6T34n4NWq0VDQwOys7Pxww8/IDc31xWU4Ofnh/r6ejgcDoSFhWH06NF46KGHEBISArlc/putL9JlSkjXjyDFO9IFWkh7efq61kdXurAM28R35F4AXJT+pOvYDuBOp5O1rgWXy3VbRqB5a9SWjKQ56SjosUjjsclB9++s50m3rV+/Hl988QWKi4sRGxuL6dOn46GHHoK/vz/4fD40Gg1yc3Px9ddfY/ny5RCJRHj00Ufx9ttvw8/Pr8Vcd7aMd3vn2ObwbugyJbxx4wZeeuklZGdnM9p69+6NF198kWjO//nnn/HRRx+hoqKixd8lEglGjx6NJUuWMM6QdXV1+Pbbb/Hll18yxgsKCsKzzz6LRx99lNFWXl6OlStXMgJ+eTweQkJC8MUXXzDOhRaLBRcvXsQLL7zAGI/P5+Oxxx7Da6+9xmgDgHfeeccV+tca//rXv9CjRw+G4qvVasycORPnz58nuhI6gi+++AI7d+5EfX19i78LhUK89tprePjhhxlns4qKCqxevRrHjx9njNerVy+8+OKLxEyV48eP49NPP0VhYSGjjSYFmzVrFiZNmoTIyEhXfDD94nfr1g1xcXEYN24c6urq8O9//xvr16/HyJEjsWjRIsyePdu1PS0sLMSnn35KlLFnz554/fXXGUYti8WC3NxcLFu2jJFVIpVKMWLECKxYsYIxXlNTE37++WccO3bM7S9ylymhn58fevbsSVS0gIAA1oNuVFQUpkyZwgjC5fP5iIuLIxpSpFIpevfuTZwMqVTKWv9QLpdjzJgxDH8cXSCVZCSgFXTu3LmMNi6Xix49ehDvBQCDBg1ijVUNCAggyi+RSPD4449Dp9O1y7jRHtCFXFsHVfN4PMTFxRHvI5fLkZmZSZzLgIAAYhoT0Pw8J0yY4EpN02q1OHr0KA4cOICBAwfi/fffR//+/eHr68vqoqIoyuXmmTlzJvr164ctW7Zg5cqVuHTpElasWAFfX1+oVCpWGVUqFWsAd7du3TB79mxG0gCfzydmlADNbpewsDBER0e3y1DU4ve41fse4O3tjczMTMYPA9Cmfyo4OBjjx49nbCloKxXpRaUj2rt3785ou7O2YWtIpVKMHDmSGBjNdh2Px4O/vz9mzJhBHLMtRUlPT2dN+ZFKpaw+0vHjx+Pw4cOs21V3kZiYiLi4OOJWis0nKpVKMWzYMLefZ0BAALKysmC322EymXD+/Hls2LABmZmZ+NOf/oSUlBTW394atBuhV69eUCqV8PLywj//+U90794dU6dOhVwuZ5WRrWwCj8dDQEAApkyZQtyOsgVn8/l8REREICAgwO1EhS5TQrY6FncDW+2JtkArjLt8nLQ/yl20x2VCglgsZnXos4HL5bp8np2VRdEetxBJjnt9ntXV1di8eTMUCgVWrFiBXr16dahMgkAgQEREBObPn4/q6mps3LgRCQkJ6NevX4dkbI87rTXooA+2D0Nb+G2akzz4zaO+vh5HjhzB1atXsWTJEvTt2/ee6pTweDwEBgZi6dKloCgK33zzDYMh4b8VHiX04IHg6tWr+PHHH9GzZ0+MGzeuU9wLPB4P8fHxeOqpp3D+/HlkZ2cTk8j/29Bl21Gj0YiysjJotVoIhUJERUUx9v12ux2NjY0uivfQ0FBibKXZbEZVVRUMBgMkEgmCg4OJQbs6nc61GoaEhMDLy4sxltPphMlkgtVqRUVFBZRKJWOLSFNYVFRUwGazITAwED4+PsSzUllZGfR6PYRCIfz8/IiRKHq9HtXV1TCZTFAqlfD39ye+hJWVlWhqanJF63Rky9se3L59Gw0NDeByuVCpVMTIGL1ej9u3b8NgMEAulyM4OJgo8+3bt6FWq8Hn8+Hn50c0Uuj1epw6dQq1tbVYvHhxp1fqGj9+PDZu3IiTJ08iIyMDkZGR0Ol0KCkpAYfDYX1+FosFNTU10Gg0EAgECA8PZ8hGvy+0dTcgIIAY3uYOuuxLWFxcjD/84Q8YN24cnnvuOaJfzWAwYO/evRgzZgwmTJiAnJwc4qG6vLwcS5cuxdixY/Hqq6+64vjuhMlkwvHjxzFmzBiMGTMGP//8M3FVtNvtKCwsxM8//4y33nqLSApks9lw/vx5TJ8+HWPGjMGOHTtYqf/ffvttTJgwAQsWLGAlcbp8+TLmzZuHMWPG4LPPPmPlk/n4448xceJEzJ8//76WEfjmm28wc+ZMPPXUU/j3v/9N7HPjxg28/PLLyMrKwrvvvkt8LgDw1VdfYdKkSZgzZw5OnTpF7JOfn4+DBw9CqVSyGqbuBUqlEgMHDkRlZSXKysrgcDhw8eJFZGVl4bHHHsP3339PfBfq6urw7rvvIisrC3PmzEF1dTWjD/2+ZGVlISsrC998843bnDKt0WVfwqCgIEyePBkTJkwgfpGAZgNBRkYGVq1a5dpakFYYf39/LFy4EGq1GiqViviFEAgESE5OxqpVqwAAqamprNbN4OBgyOVyPPnkk0TTOm2qX7lyJcxmM5KTk1kNGU8++SQeeeQReHl5sQZWR0VF4dVXX0VTUxNiY2NZLaiTJ09G//79IZFI0LNnT2KfzsCECROQnp4OLpfLyo8SFRWFN954A1qtlpV3BoArTUggELBSRNhsNtf83K8iQYMHD8b58+dRVFSEIUOGIDExERs3bgSHw0FUVBTx+SmVSixcuBDTpk2DSCQiknTxeDyEh4dj48aNAIDw8PB7SmMCuthFkZ6eDrvdzhp1QFEUwsPDXYogEAhYzeMDBw6Ew+EAl8slvsS0vycrK8s1Flsqk7e3N3x8fNCnTx+iQtOERyNHjnSVCmeLnunTpw/sdju4XC7rFsXX1xdDhw6F0+l0pc+QkJycjJ49e7Y5VmcgNDTUNedssshkMiQmJsLhcLCmAgHN9JXBwcFtRpbo9XpwuVxXv/sB2k3Q1NTk8vP279/fFflE+p0CgQCxsbEuXyBbML9MJkP//v0BNL+z93qe7TIlZFOWO0Gbee/2wrXl67tzrLZKaLce727mZbYH1xrtcaB35lidgfbI01b4nbtj6XQ6UBTVqZkIreHj4wOBQACj0Qin09nud6Y9ix2dodNZ8FhHPehy0DGznRX7yga73e7aef03w6OEHnQ5ZDIZHA4H0aDWWdDpdHA4HG4HQzwIdNl2tKGhAWfOnCEyLwcGBiImJoYY7lNeXo5r164x6vDx+XwEBwcjKSmJsf0xGo0oKSlBQUEBYzyZTIaYmBgia7NOp8PJkycZbN90JA2Jl8Rut0OtVhMtgTweDxEREayM3xcvXkRxcTGxbfDgwfD19WWs4kajEb/88gtKS0s7xONKQl5eHoqKioixo2lpaQgNDWVs07RaLS5dusQIrAf+EydMMmzQz7O8vBzl5eWdIj8JNTU1MBgMuHHjBr799ltGO22ZbW0Yop/nyZMnibGjISEh6Nu3L2M8i8Xissa6u83uMiWsq6vDunXriKb2tLQ0LFu2jPhSXb9+HatWrWIor0QiwdixY4mZBgaDAQcOHMD69esZ4wUGBuKFF14gKqFGo8G6deuIWRShoaFITU1lKCFdleqNN95gjMfn8zFx4kRWJdy1axd2795NbNu8eTPRl2UwGLB69WpcvHgRDz30EPFad5GdnY2dO3cyyJsFAgFeeeUVBAYGEpVwx44dxMUnKSkJixcvJiphWVkZjh49iqqqKuTn50Or1bpNBtwe5OTkwGQy4cKFCzh//jyjvXv37oiMjGQoocPhQGlpKT755BOGG0oqlbrYylvDbDYjPz8f5eXlRF7ettClWRSTJk3C6NGjiW1BQUHE6+Lj47F48WJisZKwsDDiQVoqleLhhx8mTkZbWRQKhQLPPPMMo1gJbRFjy6KIiIggKiGXy22TyXn8+PHEdB+gOWWHLQvk5ZdfxocffthpxoHx48dj6NChRBr8wMBA4n1oNjJS9ohEImGtwZGYmIi3334b69evx/Hjx5GXl4eBAwd2yu+godfrcezYMURHR2POnDnEd0ssFhP/TlEUevTogX/84x9EGny2BUMikaBfv344duyY2+zdXaaEPj4+rEVf2kJwcDCCg4PdukYkEiEhIQEJCQluXSeVSjFkyBC3ruFyufD392clumoLaWlpbjurRSIRHnnkEezatavTArj9/f3bLFxDgkAg6BD1v5eXF+Lj4zFs2DBkZ2dj27ZtLh9lZ+Hw4cMoLi7G+PHjiUeItkDXD2FbqNlAK6iXl5f7iQNu9fbAg07CgAED8Oijj2L//v04d+5cp41rt9vx4YcfIikpCYMGDXI7O+RBwKOEHjwQyOVyDB8+HDExMVi6dClqamruudSb0WjEsmXLUFFRgTlz5iA2Nva/3j0BeJTQgwcELpeLuLg4vPDCC6irq8P8+fNRUlLCytVzN6jVanzwwQf45ptvMGfOHPTu3fs38RUEuvBMWFVVhV27dqGwsBC+vr548sknGZY/k8mEq1ev4tChQxAIBBg/fjzRPF5bW4tDhw6hvLwcoaGhGD16NCPczGKxoKioyMXhkpWVhejoaMZ+3eFwoKamBnV1dfjpp5+QlZXFiB+12+0oLS3FTz/9BL1ej2HDhrHGj+7evRvFxcXw8/NDeno6kQ6huLgYv/zyC2pqatCnTx8MGjSIGB2zf/9+5OfnQ6FQoF+/fm1SZdwLDh48iJycHFAUhcGDB7tCslrLfODAAZSUlCA5ORkTJ04khnUdOHAAv/76K7y9vfHQQw+hV69ejD6lpaU4cuQIbty4AZlMhpdeegl//etf8corr2DJkiVISUlpN9+q3W7HrVu3sHbtWuzevRtTp07F448/3iITxOFw4ObNm/jqq6/A4/EwevRopKamMp5fQ0MDDh48iNzcXCgUCjz11FMMi73dbkd1dTXWrl0LAK66ifdi4e0yJTQYDDh8+DByc3MRFhaG2bNnM/rY7XZXnQKRSIT09HSiUcZoNOLnn3/G1atXkZycjBEjRhDHKi8vd7kAUlJSiG4Juvx3ZWUljh07hmHDhhH71NTUYO/evWhsbERISAhrQPXp06dx+vRphISEsOsLcY0AACAASURBVB7uGxsbsX//fpSUlIDP52PAgAHEfufPn8ehQ4fg7+/Pym3SGVCr1bh69SoEAgGrtdZut+PGjRu4ceNGmylVt2/fRn5+PuRyOavV02634+bNm7h69SrCw8OxcOFC8Pl8bN26FR988AH69u2LESNGoEePHqz3MpvNKCwsxNmzZ3HgwAFcunQJ6enpeO211xAYGEhc4K9cuQKKotC3b19itI7D4UBRURGuXr0KPz8/1u2x2Wx2VZxOTEy858ifLlNCpVKJ4cOHY9SoUZDJZERrmEAgQFpaGl577TVQFIWoqChiHKKPjw+efPJJqNVqKJVKIiUFn89Hjx49XExnPXv2JH5tuFwuAgICIJPJMHXqVCLxEu1qWLRoEcxmMxITE1njOidOnIhBgwbBy8uL1XoYHByMefPmoampiUi7T2PMmDFISUmBRCJx2+ztDkaNGoWBAwe6Ap3ZZH755ZdhMplc9ShIyMrKwpAhQ1ylDkgICgrCwoULYTQaIRQK4eXlhTlz5iAxMRFbt27F9u3bkZ2djfT0dMTExLhKAEgkEjQ1NbnySU+dOoXr168jIiICzz33HMaNG0cMCudwOIiJicGaNWvA4XDg6+tLtGDS1YenTp0KiqKIGR504PmaNWsANLu17rVOSJe6KEjbnDvB5/MRGRl51xfO29v7ru4OiqLQrVs3jB8/vs1+9IvHFkEB/McN8cgjj7Q5FgCiI7c1VCpVuxztKSkprF+mzkR7quCKRCJWX25HxmodVcLhcJCeno5+/fphx44d2LVrF/bu3QuDwQCDwYCGhgZ069YNJpPJVZTH19cXjz/+OJ566qk270nX2Ljbe0VXam6rWjMdvN2Zi+LvkoHbarXCYDDAaDSivr4eer0eFEWhqqrKVXdCIpFALBb/Zlmdf6vgcrmYMmUKpkyZ4mJaOHPmDP7f//t/8PX1xYIFC5CSkgJ/f/8uyzK53/jdKaHdbselS5fw2WefYevWrS4+U5lMhu+++w4OhwM9e/bE3LlzMXPmTLdr2HvQeeDxePD19UXPnj0RFBSE6OhoZGRkuM3r+d+O380y73Q6sWXLFowYMQKjR4/G8ePHMW/ePBw+fBg3b97E5cuXcfHiRWzevBlxcXH461//it69e2PatGmoqqp60OJ78D8MCgBr7YXORFlZGdauXeuyKt2J+Ph4ZGVlISoqitF24cIF7Nmzh5HZIBQK0bdvX0yaNImxLWlsbMTx48exb98+AM3uirKyMty6dQtDhgzByy+/jOjoaCiVSigUCtch3W63IyIiAgMHDoRarcaZM2ewceNGjBs3DqmpqXj//fcZJEg2mw03b97EJ598wpCdoihkZGRg6tSpxDnZvHkzKw/LsmXLEB4eztgONzY24v3338evv/5KZDPvCDZs2IAff/yRGMC9aNEiDB06lBH6VVFRgX/84x/49ddfGeMlJSVhzpw5xMD1kydPYsOGDSgqKmK0jRkzBk8++SQxkN9isWD79u04e/ZsC6NQUFAQpk+f7mJQuBO3bt3Cl19+SZQxPj4eS5cuZVidrVYrLl++jBUrVhADuAcPHoxXXnmFMZ5Wq8WJEydw4sQJt1kQqKamJpw+fRobN26EzWbDo48+imHDhiEwMLBTFdFut6OsrIw4+RKJhNVJazabUVJSgtu3b7f4u0gkIiot0Gxqrqurw82bN1FTU4OioiKEhYVh/vz5GDduHMLCwog+vjvj/8LDwxEVFYWEhATs2bMH//rXvyAUCvGHP/yhRWA4zb5F+l0URbUZg1hbW0u8DgArkZLT6URpaSmampo6LSk2ODgYPXv2JJYa8PX1JVqoxWIxIiIiiIRJ4eHhrFZWlUqFuLg4YntISAhr3CVtHEtKSmrRR6FQsMa9ymQyVhlDQkKIVk26iGhSUhLMZnOLNprqngSKouDl5QU/Pz+3Y0cp2spUUFCAS5cu4ZlnniFW0b1XKJVKjBs3jpjI6evryzqR0dHRLnP2neDxePDz8yO+IBKJBEOGDAFFUVi+fDni4uKwZMkSZGZmtjsHj8PhQKFQuCjzxGIxNm/ejOjoaDz++OMICAhwyREeHo4//elPxDHasihmZWWhT58+xDa2RVAsFmPhwoVoampym5mcDQMGDECvXr2IpQbYypF7e3tj8uTJRKY4gUDAarYPCwvDnDlziItMW0VBeTwe+vTpg5deeqkFsRJdEZkEhULBKiOfzycSNPF4PISFhWHRokVEGny2KByhUIgePXogPDy8XVbkO0Hx+XyoVCpER0cjLy8PPXr06HQeSKA5er4jER93MxmTQNe0v379OoDmrd3o0aM7FNVAURRCQ0Px6quvor6+Htu3b0d0dLSrUhGXy4VCocCgQYPcHjsmJgYxMTFuXSMUCtGvXz8EBAR0WhZFe6rrtgZFUR0ykHSE+h/4j5vB39+/3fdtbxXf1vcRCASuRba9oDmU6NLZbl17580BEOu6/9ZgMBhw4cIFbN++3eXEvZewItqX+Morr0AqlWLnzp2s20gPPHAX/5PW0bKyMmzatAne3t5YuHBhpwXyRkVFYc6cObhx4wYOHz7MStrrgQfuoMv8hA6HA2az2cXJSVIMuuKtxWIB0Lz1In3aHQ4HLBaLi3dUKBS6vt5OpxMFBQW4ePEilixZcs8hRa0xduxYbN++HcePH8fDDz/MSBy+8zey8ZPa7XZYrVY4HA4X1SJp92GxWGCz2VyUjPeLe9RoNMJisbiiQUjHEZvNBpPJBJvNBj6fD4lEQpTZaDTCbDa3WRnrzrHaylY3m80wGo1oampi3XrTJdasVqurYhVJLqvV6mJnEIvFxB2fw+GA0Wh0jSWVSlmfH815JBKJWDlt24su+xKWlZVh9erVePbZZ7F8+XKiNdRoNOLIkSOYM2cOXnjhBVy+fJl4gK+ursZ7772HuXPn4v33329RYbaxsRHXrl0Dh8PpNA6WOyGVStG/f3/o9XpitdlPP/0UL7zwAlauXEl0xwDNvDmvv/465syZgy1btjCscDS++uorLFiwAMuXL2fw3nQmVq9ejdTUVKSnp2Pz5s3EPhcuXMC4ceMQEhKC559/nlXm9957D/Hx8Rg0aBB+/PFHYp9Lly5hxowZCA0NxZgxY1jl2rx5MyIiItC/f3+cOnWKaA2+fv06Zs+ejfDwcAwcOJAol91ux7FjxxASEoKoqCh8+eWXDOIwoNnt8vzzzyM0NBQDBw5ESUkJo4/VasWlS5cQEhKCkJAQfPjhhww6FHfRZV9Cu92OhoYG1NbWQiQSsdYsNxqNqKmpgVAohMViIfaz2+2or69HTU0NAgICWvSpqanBzZs3ERcX1yH6hbuBw+GgT58+OHbsGPLz8zFu3LgW7Y2NjaitrYVQKGR1M1itVqjVatTU1BBfBhpNTU2oqakBh8Nx7Q7uB0aNGoWQkBBQFMVKt0FnO9TU1Nw16Dw0NBRisZg17jU0NBTPPvssxowZ06bRLT09He+//z7UajX27NlD/MIFBgbimWeeQWZmJry8vIhycblcxMfH44MPPgCXy8WAAQOIOzGFQoEnnngCAwYMgLe3N2sl35CQEHzwwQcAmmOF75WoqktrUUyZMsVVlYn0mReJRBg8eDBiYmJcVZlIWzA/Pz+8/PLLrqpMd5qadToddDodIiMj79v2zc/PDyKRiBFAAABz587FjBkzIBQKWd0hUVFRWL58OYxGI5RKJWsM5IwZMzB27FhXVab7BbpSb1vM0r6+vhg1ahSsVmub26/k5GTEx8e3yXitUCgwfPhw13aUDdHR0ejWrRsqKiqIDneg2VVCV+NlYwnncDgICAjA9OnTweFwIBaLicoqkUgwaNAg9OvXj7VgLJfLha+vL6ZPnw7gP1vbe0G73lKDwYDq6moIhUK3SZdoiMXiu36Z6FhBUmmuOyESiYi5gUAz05bNZmOtmd4Z8Pb2hkgkglarhc1ma6Hs7fn6ymSydiWtduvW7b7+DhrtcRtQFNUumTtzLPpMqdVqWRdUHo/XrnM/n8+/a3YHXX34btV96TLdnQXXskFv6Vpv/5xOJ6qrq7Fr167fREYBrRT3k9qAx+OBoqj7TuPuwe8DlMPhgMlkQmNjI5xOJ4qLiyGRSCAQCGAymVBTU4MjR46gurr6vhbw6CyIxWLY7fZ7Piy3BaPRCKPRyGo9+y2CbUG5m8+4o3HH9xKvfOe19+teHZ2PjoAymUxoaGiAt7c3evfu7eIakUgk0Gg0uHjxInJzczF06NB7EsBsNqO2tpZYXFMsFru2eK2h1+vR2NjIMHLQW4fWVPEymQxCoRBlZWVwOp33ZdIaGhpgsVhcWxLamNQaNGkw2/a6vr6e1TATGBhINKPb7XZUVlZCp9N1WthaaWkpamtrGZZFHo+HyMhIKJVKYqmB0tJSYhiiXC5HSEgIMT60rq7OJX9rBAYGIjg4mHiWdDgcqKqqwtmzZ1tsP2kSX9IHQqfToaKigiijt7c3IiIiGNtih8MBrVaLa9euMdwiFEVBqVQSqUZsNhs0Gg3q6upY40vZQEkkEvTv3x9bt24ldkhPTwdw7ytATU0NvvrqK+Tn5zPaYmNjMW3aNGK28rVr17Bt2zbGl00oFCI9PR3Tp09vcTCWy+VQqVQ4ffo0DAZDp/sJAaCwsBBGoxGhoaGw2+0oLi52FSO9EzweD0OGDMETTzxBHGfPnj04ceIEse31119HeHg4Y971ej3WrFmDCxcuEEmUOoItW7bgq6++YhiaRCIR3n//fYwfP54xjzU1NXjzzTdx4MABxnj9+/fHG2+8QWQZuHDhAt58801inZCZM2fij3/8IzFkzGq1Ys+ePdi/f3+LOQkPD8fixYuJc1xeXo633nqLKGOvXr3w0UcfMfy8NpsNeXl5mD17NmOB9PLywrhx4/DRRx8xxtPpdDh+/DjOnz/vdtFQCrg/n9jWMJlMKC8vx9WrVxltQqGQtfx0U1MTbt68yahFQUfxt942BAYGIjk5GT/99BPOnz+PwYMHd96PQPNKmZ2dDS6Xi549e8LhcECn0xF/F5/PR1xcHOtYVVVVxOuAZmMYaUtktVpx48YNaDSaDtMDtsZjjz2G1NRUhhuEy+UyshZoqFQqLFq0CDNmzGC0KRQKVmKq5ORkvP3228QdQGhoKGv2BZ/Px6hRozB16lTGl5At/jY4OJhVRvpr3RoURaF79+5Yu3Yt8UvIFpwtlUrRp08fpKSkIDw8nNiHDV3mooiKisIzzzxD9J1RFMVqzs7IyEDv3r2JEf58Pp9hHqZ5ahQKBbZu3YpBgwZ16iJz5coVXLhwAUlJSS5/WWpqKmut97bM10uWLMGCBQuIbWznTYVCgU2bNuGll17q2A8gICYmBlFRUUSlZ6tEK5FIkJaWRmQka6ugqJ+fH3x9fYn3aqsCMJfLRXh4OIYPH95CUduqCCyTyVhlZCsISrsghg8fTryG7V3i8/kIDAyEn5+f+8HwbvW+B/B4vLuafkng8/lun30SEhIwefJkfPbZZzh37hxSU1M7xWdot9uxadMm8Pl8jBw5Ekql0vUw26IBZENHMgro0CyBQNBpWRTtrRx8J9pb1bY12lvxl+1a0sLLhnuRsSO+P3pBcHfR/+/3OXQACoUCo0aNQnR0NJYvX46qqqp73ro5nU5s374d+/fvR2ZmJtLT0+9rHXkPfj/4n1RCiqIQERGB559/HgUFBXj33XdRWlraYUU0mUw4ePAg/va3v6F79+545JFH7msEiwe/L3QpA3dJSQmampogFAqJxTrsdjs0Gg0qKipcGc5SqZSxfTEajaiqqoJer4dUKkVISAhj+yAWi5GWlob09HTs2LEDNpsNCxYsQFxcXLu3gA6HAw0NDTh69CjWrFkDtVqNOXPmQC6Xs/qRSkpKoNPpIBKJ4OfnR7SUabVaVFdXw2g0ws/PD/7+/sTtYEVFBTQajSsE7n6xjOXk5ODmzZugKAoJCQnE5OuqqipcvHgR1dXViI6OxsCBA4k7gZycHOTn50MqlaJnz55Ew9Tt27eRl5eH8vJy+Pv7swZxFxQU4PTp02hoaEBlZSXR2KNWq3H58mUUFxdDJpNh/PjxDLkcDgcqKipw6NAh8Hg89O3bF9HR0Yx3pqmpCbm5uSgsLIRMJsPDDz/MmHOHw4H6+nr88MMPAIDevXsjJiamQ0ctGl2mhGq1Gl9//TWuXbuGoKAgvPvuu4wXz2Kx4Pz589iwYQOEQiEWL16MhIQEhhJqNBp89dVXKCwsRFxcHF588UXGhNpsNpSXl7ssfj/++CNMJhOysrKQmprq8ke1lsHpdMJms6GpqQmlpaU4ePAgdu3aBavVCl9fX/z73/9GcHAw/P39icq8c+dOXLp0CQEBAZg1axaRLr+yshLr1q1DZWUlRo0ahenTpxOV8KeffsKpU6egVCrx+OOPu13LsL04c+YMvv32WwgEAjz77LNEJVSr1di0aRMuX76MzMxM9O/fn6iEJ0+exDfffAOlUoklS5YQlbC+vh7btm3D2bNn0b17d1YlvHz5Mj766COYTCZWTp3GxkZs3boV2dnZCAoKQlZWFkMup9OJiooKfPjhh+Dz+ViyZAnCwsIY74zBYMCePXtw6NAhdOvWDenp6UQlrK2txYcffggAeP755xESEvLbUEK73Q6xWAyKosDj8VizKOjDNG2VY6sZwOfzXf1I1i+n0wkejweZTIZRo0YhMjISOTk5eOutt9C3b1+MHj0aYWFh8PHxgVAoBEVRMJvNriih3NxcHD58GNevX8eQIUMwffp0bN++HXq9HhwOh/VLSOf+iUQi1u2vw+GAQCBocy6AZoMJn8+HUCjsNCMMCY888gh69erlCponITQ0FMuWLUNjYyP8/f1ZjWX0IicUCllN9cHBwXjxxRfR0NDQpiVx4MCBWLNmDWpra/Hpp58SDR7+/v5YsGABpk+fDpFIxJpFERcXh48++ghcLpdYGAhoZol/5plnMG7cOAiFQmKQBZ1FQfsKIyMj2128hhXOe8C2bducEydOdO7YsYO1z88//+ycOHGic+3atfdyq06BTqdz/v3vf3cOHDjQGRwc7FQqlc6YmBjnyJEjnU8//bTr7yqVyhkVFeWcOnWq88SJEw9abAbsdrtz7ty5zqeeesp5/fp1t6/X6/XOPXv2OOVyubO0tPQ+SNi5KC0tdT722GPOpUuXOhsaGh60OKw4e/asc9q0ac4VK1a4dd3vyrwnlUrx/PPPY/78+dBoNMjOzsbp06dx/fp1WCwWpKSkYPLkyRg6dCh69OhxzxnTHnjQHvyulBD4j5/K19cXDz/8MAYPHuza6tF+KHp7+lsnvPLgt4HfnRLSoHlufivVXD3430WXKaFOp0NBQQGDah1oPhCHhIQQD+lqtRqlpaUMZjMejweVSoWIiAjGltFiseD27dsoLy9njCcSiVzWzdYwGo0oKipCY2Nji7/TpK8JCQkMixoddU+KAaVZo9nKaN26dYvBLE4jMTERMpmM8TW2WCy4dOkSamtr75lWgcYPP/yAkydPoqmpqcXf+Xw+pk+fjrS0NIYho7a2Fjt27MClS5cY48XExODRRx8lxnTm5uZi7969qKioYLRlZGRg7NixRFeM1WrF4cOHodFoWjwDlUqFzMxMYoxwRUUFfvjhB6KMERERePzxxxnxozabDYWFhfj8888Z75xYLEavXr0wa9YsxngGgwG5ubm4ePGi24aaLlPC+vp6bNq0ibUWxbx584gv1a1bt7Bu3TpihP+wYcPw9NNPMxTDaDTil19+wc6dOxnjKZVKzJw5k6iEWq0WX3/9NSPCn8vlIigoCO+88w5RCUtLS/HXv/6VMR5FUcjMzMS8efMYbUCz2+TIkSPEtlWrVkEqlTKU0Gg0Yu3atcjNzb1rvcf2QqvVoqKigrH48Pl86PV6Vgs120Ink8lYq9zabDZUVlYSr1Or1W0mSut0OpSXl7d4BhaLhZV6ki6FzrYYk6zXTqcTZrMZFRUVDNZ3sVjMavF1Op3Q6XQu9jd30GVKKBAIkJqaSqQFiIiIYA3g9vb2Rnp6OuMLKhQKER0dTTy38Xg8REdHE1mxfXx8WLlfaKKj1u1cLhc+Pj6s8ZXe3t7Ee1EU1SbDdvfu3VkJnNgCCng8Hvr164eCgoJOO7MOHz4cqampxJzN4OBgotlfLpfjqaeewoQJExhtMpmMlcApOjoaixcvJtaHYKu6DPynuM68efNafGmEQiFr9JJSqcSTTz6Jxx57jNEmlUqJMvJ4PERFRWHFihUMJeXxeKwxwkKhEMnJyYiKiiJmZ7SFLlPCwMBA4mTcDfHx8W0WVSFBJpNh4MCBrDXT2eDr64spU6a4dQ1FUQgPD8fSpUvdug4AMjMzkZmZ6dY1MpkM8+bNQ05OTqf5DgMDA91mTRCJRG6n7ADNi2BHIn84HA5UKhUSEhLafb1EInFbRi6XC5lMRgyyaAt0QZg7q3y1+55u9fbAAw86HR4l9MCDBwyPEnrgwQNGl7oorl69ivr6ekgkEqSmpjIMCzabDTU1NSgsLASPx0OPHj0gl8sZLgiagr6pqQlyuRxxcXGMfTjN+E1z2sTHxxMJi6xWK/Lz86HVauHl5YXIyEiGldbhcLjo9a1WKyIjIxEYGEgMYL569So0Gg2kUilCQ0OJ8YcajQa3bt2CXq9Ht27dEBERQTT63LhxA7W1tRCLxQgJCXG7RFx7sW7dOuzevRtCoRCzZ88mnt2vXLmCDz/8EFeuXMHw4cOxYsUKYuLrZ599hu+++w6+vr547rnnMGLECEafgoICrF27Fjk5OYiPj8eXX35JlGv37t1YvXo1jEYjamtriUVhi4qK8Pe//x2nT59GYGAgvvnmG4ZcdrsdOTk5WLx4MSiKwosvvogxY8YwjEDV1dX4+9//jiNHjiAoKAgfffQRqwvj6aefBtBM9vzYY4/dlSu3LXSZEtbW1mL9+vXIy8tDaGgoPv/8c8ZLbLFYcPbsWXz88ccQCoVYuXIlUlJSGJPa0NCAdevWoaCgAImJiXj99dcZSmi1WnHlyhW8+eabAIA//vGPyMjIYFgdTSYTNmzYgKtXryI6OhpLly4lKmFhYSHef/99NDU14bnnnsPYsWOJSrht2zacO3cOwcHBeP7554kPp6ysDB9//DHKysowYcIEzJ07l6iE33//PY4cOQJ/f3/Mnz//vilhSEgIevXqBT6f32bV2x49ekAikSA6Opo1nC8kJARpaWnw8vJitVrKZDLEx8eDw+G0aUn09/dHnz590NjYiLNnz7IWTY2JiYHdbmcw79GgS9v17dsXPB6PNXWMtrhrtVr4+voSAznoOok0iVW3bt26hoG7M6BQKDB06FAMHjwYXl5exIfI5/ORlJSEBQsWgKIohIWFESfL29sbU6ZMgVqthkqlIprzafcAzeESHx9PVBqBQIAJEyZg6NChrOzfdHbB3LlzYTabkZSUxJpFMHr0aPTu3Rve3t6s7NmBgYF44okn0NTUhJiYGNYM/eHDhyM2Ntb1Vb1f6N+/P3r27Akul8vKFObv748ZM2bAZDJBJpOxumsyMjKQlJTUpjlfpVJh8uTJMBgMbUYsJSYmIigoCNXV1QyiLxoKhQKTJk2CXq93Zda0BofDQWhoKBYvXgwOhwNfX1+i4shkMmRlZWHYsGGgKIo4F3QAxuLFi133v9eoqy5TQh8fn7u6DPh8PqKiolhr0dPw9vbGkCFD2uxDURSCg4MxceLENvsJhcK7jsXlchEQEICxY8e22Q/4D0VkW/Dz88PDDz98136pqalITU29a797RXtKD7SXD0ehUNyVIr694YLe3t7w9vZusyS2UChk/XrToL9ebJFLNPh8/l0rQ9P1Ou42ljvwGGY88OABw6OEHnjwgNFl21Gn0+mqTtsaXC6XlXPS4XDAZrOx8lSSzgBOp9N1XWtwOBxWij/n/1FbsPFUslXUdTgcrLUI2WQEmi1tbNn3fD6fOB9OpxMWiwV2u73TCtLodDoYjUYit6uXlxdEIhHRkq3T6YhFOQUCAaRSKfHcZTKZYDAYiPMlFovbrO9hMBgYdP00lSaJXoKuzkuSkc/nE+sZ0u+pRqNhzC8dyE86K9LVo00mk9uEYl3qorh06RKxLoBCoUBcXBxr7YJr164xYg15PB6CgoIQHx9P5KopKyvDrVu3GOOJRCJER0cTS7yZTCZcvnyZmOkhlUrRt29fYgB3Q0MDcnJyGNdwuVyEhISge/fujDagmeKflE0ANBtLvL29GS+/1WpFdnY2qqurO43xbe3atfj6668ZpQZEIhHeffddjBs3jmHOr6iowPLly3Hw4EHGeP369cPy5cvRp08fRtvx48fxzjvv4Nq1a4y2GTNm4LXXXiPS4JtMJnz99dfYsWNHi8UpLCwML730EmbOnMm4prCwEH/5y1+IMvbq1QurV69m0OBbrVacOXMGTz/9NKNehpeXF8aOHYs1a9YwxtNqtTh48CCOHj3qNhVmlylhdXU1Pv/8c5w5c4bRlpaWhqVLlxKV8MqVK1i1ahXjZZVIJBg7diyWLVvGUEKdTod9+/Zh/fr1jPGCgoLw3HPPEZVQrVZj7dq1jNLUNPPb+vXrGQYM2m/06quvMsbj8/mYOHEi/vjHPzLaAOC7777Dnj17iF+0TZs2oUePHsTf9s477+DixYsYNmwYcVx3kZGRAalUyihFQFEUevbsSfyiyeVyjB8/HklJSYy24OBgVstwVFQUZs+eTVyMk5KSWAO4+Xw+evfujeHDh7cw0sjlcqIMQLMVlk3GgIAA1gDu0NBQLFy4kBFcLxAIWOOYaQbB2NhYt11JXaaEISEhmDx5MiNnDWg2DbNZuNLS0vDhhx8SKwbJ5XKiq8Db2xvTpk0j1qwXCASsk+Tn54cVK1ZAr9e3+DuHw4FAICCmWvH5fCQkJGDTpk2MNtoczoZ58+Zh8uTJxLaoi5I4/AAAC8xJREFUqCjidtTLywsff/wxli9f7jZ7NxtSU1ORkJBA3I5KpVLiyu7l5YWRI0cSs0D4fD6rbCEhIZg0aRLxqCASidrMHklMTMSsWbNabAd5PB6rpdXHx6dNGUlbWC6Xi27dumHWrFmMxbEtZm6BQIDIyEiEhISwZumwocuUUCwWu10yCmhe6dylmKedznczXbdGR0zPdPmzxMREt64DOlaJl8/nIz4+HgqFotOyKNpTnbY1eDxeh5KK6eq7HYFIJIJCoWh3FgWd2eAO6LO/uxEwd1L0u8tL5LGOeuDBA4ZHCT3w4AGjy7ajtEnbarWCx+MRzby0+Z0m2JXJZETWM7vdDoPB4KpPT6LKp03NtIVLJpMRXQwOhwN6vd41Fk1Q3Bq0udvhcEAikUAoFBLdFXf+RrFYTDyzWq1WGI1G2Gw21zmINJZer4fFYnGde+41RpENdKVemsaDlODb2NiI8vJyNDY2ws/PjzV+tLS0FNXV1RAIBAgKCiJaOpuamlBZWeki/2XbyldXV6O4uBg1NTUM6g0aOp0OVVVVqKurg0gkQkpKCvFd0Gg0yM/PB5fLRUREBFQqFeM50zU0a2trIRQK0b17d8Y23el0Qq/Xu3hrwsPD4efnd0/PpsuUsLGxEQcPHkRlZSUUCgWmT5/OmCyr1Yrr16+7zLyjR49GSEgIw0Ko1Wpx6NAh3L59G0FBQRg1ahTDqmaz2VBSUoL9+/cDaM5ij4qKYiiF1WrFwYMHUV1dDZVKheHDhzMO1nSp5gMHDsBkMiEjI4PVanjs2DGUlpZCLpdj8ODBxADluro6F2lRcnIyBgwYQFRWmhPVy8sLGRkZiIiIaGOGO44ff/wR3333HYRCIebOnYtJkyYx+pSVleG9995z0eC//fbbxLPd7t27sWXLFiiVSixevJiohBUVFVizZo2LBn/Lli1EuU6ePIm//OUvMJlMaGxsJIbw1dTUYM2aNS4a/J07dzLkcjgcuHbtGl544QUXDT6pZoVGo8Hnn3+OgwcPolu3bvjiiy8YSmi321FWVoYXXngBQDMN/pQpU34bWRRqtRqHDh3C2bNnERERgalTpxJZ0vLz87FhwwaIxWIkJycjMDCQoYQajQY//fQT8vLy0KtXL5eJ/U5YrVYUFxdjw4YNAODi/mj9sptMJuzbtw95eXno3r07kpOTGUpot9tRUVGBLVu2QKPRQC6XIzY2lqiER44cQXZ2NsLDw13WstaorKzE7t27UVRUhOnTp6NPnz5EJTx16hT279+PoKAgV8rT/cDAgQPh5+fnckmQEBAQgCeeeAJ1dXUIDw9n9YUNGTLEVaeDjV/H398f06ZNw5AhQ9r0dSYnJ2Pp0qWoq6vDli1biLsFX19fTJ061fUOsBX+DAsLw7Jly8DlctG7d2/is/Py8sKjjz6KlJQUyGQyokGQjiNetmwZACAlJeWe6lAA6Doa/E8//dRpsVicJpPJaTabiX0dDofTZrM5TSaT02QyOe12O2s/eiyLxeJ0OBzEfna73TWWzWZr11hs92w9Fts92zuW2Wx2mkwmp9VqJfZxOp1Oq9Xqmq875e9sGny73e602Wxt/i762dhsNtbfRcvWnrHu7McG+p5FRUWsNPjujtWWXO7IT5qL/3oafNr0e7c+7aka256xgOZV627m8M4cC0C7x2rPGYIueHO/0R6TOv1sOmus9jDFted9cHesu6Ez56K96JB1VKPRMHxUFouF9fDsgQcesMNtJXQ6nTh69Chyc3NdlketVovz58/j5MmTnS6gBx78r8PtvY7T6URxcTF27tyJ4OBgWCwW5OXl4dixY8SAXRoWiwX19fVEdmKRSASpVErc7hmNRmi1WsaXl8PhQCwWQy6Xs7owtFotYzyKoiCTyYiHaZvNhsbGRmLUPUVRRI4a5/+5VUixkHQyKVvEj0ajYcRr0lCpVMQtq91uR01NDQwGQ6dtVc+dO4eCggJi7GhGRgbRqtzY2Ijs7GyUlJQwxgsKCkKfPn0QFBTEaCsuLkZOTg5xvnr06IG0tDRi/KjdbkdeXh6++uqrFqFt3t7eSE5OZgRiA83GwJycHBQXFzPa/P39MXjwYIZhyG634/bt2zhw4AAxdjQyMhJDhw5ljGc2m1FSUoKioqKuix09evQoVCoVzGYzbt26BafTid69e7P2r6+vx/bt21FYWMhoCw8Px/jx44lB1UVFRfj+++8ZmQ0CgQBpaWnIyspivCBGoxEnTpzAL7/8whiPjickydrU1IRt27YxXiyaePa5555j1BlwOBwoLy/HF198wRiPZstmIz0+ePAgzp07R2x78cUX0a1bN2Kp8PXr1+PKlSvEF68jyM/Pxw8//ACNRtPi7wKBAMHBwQgPDyfO8fHjx4kB+QkJCYiNjSUqYV1dHfbt24fS0lJG26hRo5CYmEhUQofDgRs3bmD37t0tZAkICIBCoSDOhV6vx/Hjx3H69GlGW2xsLHr16sVQQpo6f/fu3YxFSSKRYPDgwUQlpF1iarWauMC0hQ4poUgkgtlsRk5Ojquabnh4eJuGC7PZjKqqKty8eZPRJhAIiLToQLMztqSkBDU1NQwZQkJCiBkINpsNDQ0NxHv5+fmxnl2tVisqKysZ13G5XFdwQGs4HA4YDAbivSiKajMWtba2lngdANZ6BjabDcXFxWhqanI7b40NgwYNQkxMDGPl53K5iI2NZQ2SnzFjBpFB3MfHh+gfBJpTj55//nlGmhDQ/AVlM/fTC9qsWbNaLIRisZi4eANw+aNJVCLe3t5E9wiPx0N4eDiWLVvGmF+KoliDswUCARITExEWFsYqDyvcsqX+n3n255//f3tnr9M4EEXh47ENIQJDLEAGUSCBkBAlaZEQNRU8AR0Nb8NrIPEGS0ONaNKB0uAkQMCxUfwT/2zhHW8C40ACyOzqfvXo5iaeY0V35p77K9nY2EhkWU4AJLIsJ9VqNbm4uHiz/idN6v1foEm9P5NxjyhGLsxIkoTd3d0Br8X5+Xns7++/a5hEEMRbxr7AfXJygu3tbZRKJezt7eHo6Igm2xLEGIxdmDEMA8fHx1heXsbBwcHIfXEEQaSMLUJFUbCzs4OtrS3ouj60XB5FETqdDm5vb+H7PhRFEV54TZIEnufBcZzMNVnU+RCGIRzHQa/Xg6qq0DQt9+iAF2E0TRN2PnCLex6Ld1u8JggC2LaNOI4xPT2d2/lgWRZ6vR4URcm6LUSxXl5eEIYhyuWycBgokJ6/ep6XmRnxDnL+3T7zz4M3ofKJtO12G4wxLCwsCH1DPc+DaZpwXReapmFlZUX4+a1WC09PT5kHkKip1vd9mKaZmf+ura0Jc3x+fkaj0YDv+3AcB/f39zg9PR14PkEQZLFUVcX6+npuR0q9XockSTAMA3Nzc28qz2EYotFowLZtTExMYHV1VbgXPM/LqvyLi4vQdR2yLMM0Tdzd3Y0+Vm2k1a/QdR2VSmXoZmCMwXVdnJ+f4/LyEmEYQpblD4sw76zMtu1MOKJ5FUD6sN8TYfKnzYXnNTs7K7yS9FERdjqdrP1I5OYFpFVYXt2cmpoSjsUG/oqQMYaZmZmB3+Lq6mqsbn4grQBWKhVUq1XUajV0u124rgtJktBsNoUVSv7iCIIApVIJzWYzN+dutwtZltFqtYR2Fbxdzfd9qKoqNNYCUnc127bBGMs8cK6vrwfW8BYz/rKyLEuYl+/72ec8Pj4Kn18URQMvvna7ndvWxo8hHh4eUC6XwRhDEARYWloaeSailCRf5JuXw83NDc7OzlCv17+spE6kRzSbm5s4PDwc+XA4iiJYloVarZbZQ/JtIElSrtUiX8cYy71j2R+LMSYURH+sYfcw4zhGHMfZ/dC8vHi8YbGSJMn2X17+r/Maln9/rP77q5OTkzAMYyQhfrsIoyjK9fIkPge/4E0FsX+bbxchQRDDIY8ZgigYEiFBFAyJkCAKhkRIEAVDIiSIgiEREkTBkAgJomBIhARRMCRCgigYEiFBFAyJkCAKhkRIEAVDIiSIgiEREkTBkAgJomB+A6XvwNaaBopvAAAAAElFTkSuQmCC)
What is the reading of the scale when the ball is fully immersed?
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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)
What is the reading of the scale when the ball is fully immersed?
physics-General
physics-
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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)
What is the mass M of liquid which overflowed while the ball was being pushed into the liquid?
A cylindrical container of length L is full to the brim with a liquid which has mass density r. It is placed on a weigh-scale; the scale reading is W. A light ball which would float on the liquid if allowed to do so, of volume V and mass m is pushed gently down and held beneath the surface of the liquid with a rigid rod of negligible volume as shown on the left.
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)
What is the mass M of liquid which overflowed while the ball was being pushed into the liquid?
physics-General
physics-
A cubical sealed vessel with edge L is placed on a cart, which is moving horizontally with an acceleration ‘a’ as shown in figure. The cube is filled with a ideal fluid having density r. The gauge pressure at the centre of the cubical vessel is
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)
A cubical sealed vessel with edge L is placed on a cart, which is moving horizontally with an acceleration ‘a’ as shown in figure. The cube is filled with a ideal fluid having density r. The gauge pressure at the centre of the cubical vessel is
![](data:image/png;base64,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)
physics-General
physics-
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,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)
In which of the following situation(s) of static equilibrium must the density of the gray liquid be greater than the density of the black liquid? (circle all appropriate cases)
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,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)
In which of the following situation(s) of static equilibrium must the density of the gray liquid be greater than the density of the black liquid? (circle all appropriate cases)
physics-General
physics-
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,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)
Which of the following situations does not show static equilibrium of liquids.
The figure below shows four situations in which a gray liquid and a black liquid (which we known nothing about) are in a U tube.
![](data:image/png;base64,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)
Which of the following situations does not show static equilibrium of liquids.
physics-General
physics-
An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure. The efficiency of the gas cycle is :
![](data:image/png;base64,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)
An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure. The efficiency of the gas cycle is :
![](data:image/png;base64,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)
physics-General
physics-
The initial state of an ideal gas is represented by the point a on the P-V diagram and its final state by the point e. The gas goes from the state a to the state e by three quasi stationary processes represented by
i) abe
ii) ace
iii) ade.
The heat absorbed by the gas is
![](data:image/png;base64,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)
The initial state of an ideal gas is represented by the point a on the P-V diagram and its final state by the point e. The gas goes from the state a to the state e by three quasi stationary processes represented by
i) abe
ii) ace
iii) ade.
The heat absorbed by the gas is
![](data:image/png;base64,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)
physics-General
physics-
The P.V. diagram of a certain process (Carnot cycle) is as shown in the figure.
![](data:image/png;base64,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)
The process is represented as
The P.V. diagram of a certain process (Carnot cycle) is as shown in the figure.
![](data:image/png;base64,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)
The process is represented as
physics-General
physics-
The following graphs shows two isotherms for a fixed mass of an ideal gas. The ratio of r.m.s. speed of the molecules at temperatures T1 and T2 is
![](data:image/png;base64,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)
The following graphs shows two isotherms for a fixed mass of an ideal gas. The ratio of r.m.s. speed of the molecules at temperatures T1 and T2 is
![](data:image/png;base64,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)
physics-General
physics-
A volume V-temperature T diagram was obtained when a given mass of gas was heated. During the heating process from state 1 to state 2, the pressure :
![](data:image/png;base64,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)
A volume V-temperature T diagram was obtained when a given mass of gas was heated. During the heating process from state 1 to state 2, the pressure :
![](data:image/png;base64,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)
physics-General
physics-
Two rods of same length and cross-sectional area are joined in series. Thermal conductivity of the rods are in ratio of 2 : 1.
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)
The ends are maintained at temperatures qA and qB as shown with qA > qB and sides are thermally insulated.
Which of the following graph represents temperature gradient (dT/dx) against x in steady state
Two rods of same length and cross-sectional area are joined in series. Thermal conductivity of the rods are in ratio of 2 : 1.
![](data:image/png;base64,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)
The ends are maintained at temperatures qA and qB as shown with qA > qB and sides are thermally insulated.
Which of the following graph represents temperature gradient (dT/dx) against x in steady state
physics-General
physics-
Select the correct statement on the basis of the given graph :
![](data:image/png;base64,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)
Select the correct statement on the basis of the given graph :
![](data:image/png;base64,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)
physics-General
physics-
The load versus strain graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line
![](data:image/png;base64,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)
The load versus strain graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line
![](data:image/png;base64,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)
physics-General
physics-
The distribution of relative intensity I (
) of blackbody radiation from a solid body versus the wavelength
is shown in the figure. If the Wien displacement law constant is
mK, what is the approximate temperature of the object?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQAAAADZCAYAAADPNO41AAAgAElEQVR4nO3deXzU1b3/8desmclk3/d9I4SdSAx7wAICAay2VLR6rUXqxVK72eX2lnprW+Wqt9rWSq1iRVEpskhkk30RSQiEJZElJIGEbGSSSWZff3/4m7nlqpBAkkky5/l48FAgme9hMt/393zP95zPkbhcLheCIPgkqbcbIAiC94gAEAQfJgJAEHyYCABB8GEiAATBh4kAEAQfJgJAEHyYCABB8GEiAATBh4kAEAQfJu/rAxiNRqRSKQqFAplM1teHEwShB/q0B+Byubhw4QJ79uyhra2tLw8lCMIt6LMAcLlcWCwWVq1axdNPP83u3btxOp19dThBEG5BnwWAXq/n/fffZ9++fVRUVPDmm29SXV2NWHwoCANHnwSA1WqloaGBP/7xj7S1tWE2mzl58iSvvfYaFotFhIAgDBB9EgAmk4ndu3dz+vRprFYrUqkUrVbLxo0baW5uxuFw9MVhBUHooT4JALPZTHNzMxKJhLCwMCIiIvDz88NgMKDT6cRYgCAMEH32GFAul5OcnExRURE1NTVERUVx5MgRJBJJXx1SEIQe6pMAkEgkhIeH85vf/Iaamhra29uZP38+UVFRSKVi7pEgDBR9EgCBgYHMnDmT6Oho3nzzTWQyGYmJidxxxx0EBASICUGCMED0SQCoVCoyMzORSqWek93f35+UlBScTqe4DRCEAaLPbgG+6iQXtwCCMHCIs1EQfJgIAEHwYSIABMGHiQAQBB/W5/UAfJHD4cBisaDX67FarTidTuRyOSqVisDAQORyuXgSIgwIIgD6gF6vZ9++fbz99tucOHGCzs5OYmNjmTNnDg8//DCpqakolUpvN1MQRAD0ts8++4zVq1fz8ccfk5eXxw9/+ENiY2O5cuUKR44c4dvf/jbLli1j1qxZxMXFebu5go8TAdCLqqqqeOWVV6isrOT73/8+kyZNIjIyEoVCgcViYerUqWzZsoV169ZRV1fHQw89RGpqqrebLfgwEQC9wOFw0NLSwl/+8heqq6t59NFHKS4uRq1WX3evHx4eTkxMDEFBQZSUlOB0OlmxYgUhISFierTgFeIpwG1yuVwYDAY2bNjAsWPHuO+++1i4cCH+/v5fGOiTSqVERUXxyCOPUFxczEcffcS2bdswGo2iSIrgFSIAbpPFYuH06dOsWrWKe++9l3nz5qFSqW74PRqNhoULFzJ79mx+/etfc/78eWw2Wz+1WBD+lwiA21RbW8uzzz7LxIkTWbhwIaGhoTf9HolEQmRkJA8++CAjRozgD3/4AzU1Nf3QWkG4ngiA29De3s7Ro0dpaGjg8ccfJy4uDrm8e8MqSqWS+Ph4li9fTk1NDYcPH6a9vb2PWywI1xMBcBvq6urYuXMns2fPZuzYsWg0mh59v0ajYeLEiXzta19j27ZtXLhwQYwFCP1KBMAtslgs7N+/H5lMxgMPPICfn1+PX0MikeDn58dDDz2ExWKhpKQEs9ncB60VhC8nAuAWVVdXc/z4cXJzc8nOzr7lx3hSqZTMzEzuuusuzp07R2VlZS+3VBC+mgiAW+B0Onn//fdRKBQsWrTotoucSKVS7r77bsLCwnjrrbdwOBziVkDoFyIAeshms3Hu3DkOHjzI+PHjSUxM7JXXjYuLY+LEiVRUVHD8+HGsVmuvvK4g3IgIgB4ym818+OGH+Pv7M3r06B4P/H0VtVrNmDFjiI6OZt26dej1etELEPqcCIAecDgcdHR08O677zJ79mwyMzN79fXj4+NZsGAB//znP7ly5YqYHCT0OREAPaDT6di+fTsKhYKpU6d2a9JPTwQFBVFQUEBaWhrr16+ntbW1V19fEP4vEQA90NDQwJYtW1i8eDGxsbG9voDHvZXagw8+yI4dOzhx4oR4LCj0KREA3dTZ2cnp06fR6XTMnz+fwMDAPjmORqNh7ty5pKamsnHjRqqrq/vkOIIAPQwAp9Ppszv7XrlyhY8//php06aRlJTUZxV95HI50dHRLF26lPr6ejZv3kxXV1efHEsQehQAHR0daLVarFarT41Q22w2du7cSVNTE8XFxX2+dl8qlTJlyhRGjx7N/v37OXPmjE+930L/6VEAHDx4kOeff54DBw7Q2dnpM9t8uxfrxMfHM2LEiH4p3qFUKnnooYeIiIhg1apVGAwGn3m/hf7TowDIzs5m0aJFBAUF8dZbb1FSUkJ1dTUmk6mv2jcgbN26lY6ODoqLi/utmKdEIiElJYWFCxfS1NTEW2+9hV6v75djC76jRyXB0tPTPc+m/f39OXToELt27SI9PZ2pU6eSkJBAYGDgLS2MGYgcDgdtbW1s3LiRESNGMGrUqH4t5+3v709BQQHTp0/njTfe4M477yQnJ+emBUcEobt61AMwm81otVqamppoaGjg+PHjnDt3jurqasrLy9m2bRv19fVD5kplsVg4cuQIOp2O/Px8YmJi+r0NMTExPPzww7hcLt544w2am5vFeIDQa3rUAzh69CglJSVcvnyZs2fPMnfuXH7zm98wbtw45HI5Bw4c4B//+Afz589n/PjxfdXmfmM0Gvnggw+Ij49n1KhRXqnlr1AoiImJ4cknn+T3v/89+fn53HvvvaIXIPSKHvUALl++zLZt28jKymL9+vX853/+J2PHjvVUwYmIiODUqVNs2bKlTxrbn2w2G01NTWzfvp1Zs2aRnJzstba4awiOGzeODRs2cOLECa+1RRhaehQAKSkp/Md//AdPPPEE2dnZBAcHY7FYaGlpwel0Ehsbyze+8Q1mzZrVV+3tN+3t7WzdupWQkBBmzJhBUFCQ19oilUpRq9U88cQTOBwO1q5dS3Nzs9faIwwdNw0Ad9nr9vZ27HY78fHxqFQq9Ho9Wq2Wq1ev8u6773L27FnUajXFxcWMHTu2P9reZ1wuF/X19ezZs4dp06Z5NvfwJolEQm5uLnPmzOHChQts374du90uxgOE29KtMYDLly9TUVFBeXk5TqeTCxcueP5Oq9Vy+vRpQkNDSU9P77Xlsd5kMpmorKykrq6OFStW9Nm0355Sq9XMnTuX2tpaXnnlFQoLC0lOThb7DAq3rFsBEB8fz969e9mzZw9BQUHU1tZ6/k4mk5GUlMSYMWO8fpXsLfX19Wzfvp34+HimTZuGv7+/t5vkkZSUxMKFCzl27Bgvvvgiv/71r4mKihK7DQu35KYBIJFICAgI4P777ycnJ4fw8PAvVMGRyWT4+/t3uyT2QHfw4EHq6up49NFH8fPzG3An1/Dhw1m+fDnf//73KSoq4q677iI4ONjbzRIGoRuOAVitVlpaWrBYLPj7+5OXl4darcZoNF73q7Ozk8rKyiFRwOLatWscOnSI4OBgpkyZMiD37HOXE7/vvvtYvXo1FRUV2O12bzdLGIRueMnu6uri73//O3fccQcTJkzg9OnTbNmyBaVSiVQqRSKR4HK5kEql5Ofnk5mZOejvRy9evMjVq1cZN24cCQkJA+7qD5/3uEJDQ/nud7/LD37wAzZv3kxiYqLYaVjosRv2AGw2G1qtlq6uLux2OzabjYqKClwuF35+fiiVSpRKJRKJxPPfwczpdPLxxx/jdDqZOXPmgB7T8PPzY/jw4Tz22GNUVFSwadMmjEajt5slDDI37AHExMSwatUqz+8nTpzIq6++SlZWFhKJBKfTicvlwuFw0N7ePqiv/k6nE6PRyJYtW8jPzyc7O9vbTeqWOXPmcPToUbZs2UJhYSH5+fm3XaZc8B3d/qS4XC5cLhcajYb29nYcDgdnz55l8+bNfPrpp0RERAzqD57JZGLHjh0YjUYKCgqIjIz0dpO6Ra1W8/DDDxMbG8sf/vAHdDqdWDYsdFuPztgTJ07w8ssv09jYSGVlJX/6059Yt24dJSUlXLx4cVAPAhoMBt5//32Sk5MZMWLEoOnNSKVSUlNTWbx4Ma2trbz55pvodDpvN0sYJLodAE6nE5PJxKhRo4iJiWHjxo1otVruv/9+iouLKSsrG7QBYDabqaur4+DBg8ydO7fXNvvoLxqNhvHjxzN79mzWrVvH2bNnh8yKTKFv9SgApFIpcXFxNDY28uGHH7Jw4UIKCgoIDAyko6Nj0NYL7Ojo4MMPP0SlUjFz5kxCQkK83aQei46O5tvf/jZBQUG8/PLL1NTUiEeDwk11OwAUCgVhYWGsW7eOJUuWkJeXR15eHmfOnOHll18mLCxs0I4B1NbWeq7+oaGhA/LZ/83IZDJiYmL4/e9/T2VlJe+88w4dHR3ebpYwwPVo6l5eXh7PPPMMOp2O4OBgNBoNCQkJZGZmIpfLB2UlIJPJxJkzZ6ivr2flypUEBAR4u0m3TKFQMGLECH70ox+xZs0a1q5dy+OPPz5oxjOE/tejAHC5XJjNZhobG6mtrfU8GZDJZCgUCiIiIgb0s/Mv09TUxLFjxzzrGQZjiLlJJBL8/PyYPXs258+fZ9u2beTk5DBz5swhM01b6F3d/lS4XC7OnTvHa6+9Rltbm6eb7B4bWLhw4aAcAzh9+jTV1dWezT4G+2Qm+Hz+xuLFi2lsbOTPf/4zqamppKSkDOpwE/pGtwPA6XRy5MgRysrK+PnPf05ISAhSqRSHw4HVakUqlQ66MQCr1cr+/fuRyWRMnjzZ283pVcOGDePf/u3f+NnPfsarr77Kj370I2JiYgbl+IbQd7odAFKplKSkJGbPnk1xcfF1f+d0OjEYDIPuCuOubZiQkEBubu6QuPq7KRQKxowZww9/+EP+/d//nREjRnDPPfeIVYPCdXrUA0hISGDHjh3s2rWL4OBgzxVfIpGg1+spKCgYNMUqXS4XBw4cwGKxMGPGjEEXXt3h7+/PtGnTWLZsGatXryYkJIS5c+eKQUHBo9sBIJFIqK6uprKykubmZs86eafTiUKhYN68eYNmCqp7UtN7771HSkoKd9xxx6C7fekOmUxGcHAwDz30ENXV1axbt47IyEgmTpw4pHo7wq3r0S1AcnIyubm5zJgxA5lM5nkKYLPZiIqKGjQnkdVq5eTJk9TV1XHPPfcQFxfn7Sb1GYVCQVpaGitWrOC5557jlVdeISoqivT0dDEeIPTsMWBOTg5PPvkker2exMRE5HI5TqfTEwaDpWtpMBj46KOPiIyMJC8vb0jUMbyZsWPHsmTJEl544QX+/Oc/86tf/WrQTnoSek+PLtnNzc289NJLTJ48mU8//RS9Xk9paSklJSWoVKpB0610B8DYsWNJSkrydnP6hUwmY+bMmTz22GNs3bqVN998k/b2dm83S/CybgeA3W6nqqqK1tZWnnjiCQICAggICCAuLo6dO3eye/duzGZzX7a1VxgMBiorK6murmbevHmEh4d7u0n9xt/fn5kzZ7J8+XJee+01duzYwbVr17zdLMGLejQIqFAouPfee5FKpSiVSmQyGRaLhebmZi5dusTEiRP7sq294tq1a2zZsoVhw4aRnZ09aJ5a9AapVEpYWBiLFy+mpaWF119/HYD58+d7deMTwXt6NAgYHh6OXq+ns7MTiUSCVCpl//79tLa2DopBQJfLRXV1NadOnWLu3LkEBgYO+Db3NoVCQWRkJN/73vdobGzkvffeIyoqiilTpgyJsm5Cz/SoBxAXF0d5eTm7du1CoVDQ1dXF1atXGT58ONOnTx/wV1Oz2cyZM2dobW1lzpw5A6ref3+Sy+UkJSXx05/+lN///vc899xzREdHM2zYsEG3lkO4PT16ChATE8ODDz7IpEmTKC8vx+FwkJqaSnZ2NmFhYQP+6nHlyhWOHTtGeno6Y8aM8fkR8OzsbJYuXcpzzz3Hz372M/72t7+J6cI+pkf93/Lyci5evEhGRgbFxcUsWrSI1NRUNmzYwKVLlwZ8RaDS0lIaGhr41re+hVwuH/CB1ddkMhljxozhxz/+MZ2dnTz99NNcuXJl0EzoEm7fTXsALpeL2tpaysrKOHr0KBKJ5Lr6821tbVRWVhIZGUlsbOyA7EK6XC70ej179+4lODiYCRMmeLtJA0ZAQAAjRozg8ccf56WXXuK1117j4YcfJi0tzefGR3xRtwJAqVRSXV3NsWPHcDgc120Oarfb0Wg0A7oqsHvwr7a2ltGjR/vMs//uCg0NZf78+TQ1NbFhwwakUinf+c53SEpK8vle0lB30wCQSqXEx8fz6KOPkp6eTkREBDk5OZ5tqWUyGWq1GrVaPWCLTjidTvbs2YPT6WTq1KkDfrCyv7n3f3zsscfQ6/Vs3ryZrq4ufvWrXxEcHCzGBIawbp+xYWFhFBcXe058m8123f9XV1eTm5s74FbVuVwuLBYLGzZsIC8vjxEjRni7SQOSRCLB39+f5cuX43A4WLduHYBnyrDoCQxNPZoHcPnyZf72t7/x6aefev7c6XSi0WhYunTpgNxNx2Qy8cknn9Da2sqUKVOIjo72dpMGLIlEQnBwMI888ghKpZK1a9cilUpZsWIFiYmJIgSGoB7VAygtLaWsrIzZs2cTEBDgWQ7scDg8vx9o9Ho9JSUlJCQkkJWVJbr/NyGTyYiLi+PBBx9EJpOxceNGAgMDeeCBB8TA4BDUo5qAUqmUKVOm8KMf/QiFQuHZHdhisdDY2DjgxgDcexbu3buXu+++e8Du9jvQKBQK4uPjWbZsGQqFgi1btuB0OvnOd75DYmKiCIEhpNtnrEwmIzc3lzNnztDW1oZarfacTA6HA71e7xkTGCiMRiPHjx+npqaG4uJiwsLCvN2kQcNdTGT58uX4+/vz9ttv09bWxsqVKwkLCxMDg0NEtwPAbrdz6tQpduzYwYcffohGo/FcCYKCgnjkkUdIS0sbUDUBGhoa2Lx5MxMnTiQ1NXVAtW0wcG/7/uCDDxIQEMBf/vIXfvKTn/Db3/6W2NhYEQJDQI96ACkpKeTm5nL33Xd7Tn53QdCBtrDG6XRy9uxZLl68yGOPPYa/v7/o/t8CiUSCRqNhzpw5hIWF8Yc//IGnnnqKn/zkJ+Tk5IgxlUHuhgHgdDqxWCyeYh+5ubk8+eSTZGVlXfc1Npvtur0CBgKtVkt5eTkul4sZM2aID+ptkEgkhIeHU1hYyIoVK1izZg0vvPACS5YsobCwkMDAQG83UbhFNwwAq9XK6dOnSU1NRS6XI5VKSUlJwWq1Xvd1TqcTo9HYpw3tqUuXLnHy5EkKCwtJS0sTV//bJJFICA0NZcGCBURGRvLCCy/w8ssvA5Cfny8mDA1SNwwAk8lEaWkpe/fuJTQ09Evn+TudTux2O9HR0WRkZAyI+2yn08n27duxWCzcc8894uTvRQqFgqlTpxIeHs6f/vQnfvzjH7N8+XLuu+8+EQKD0E1vATo7O/nwww+Ry+Vf+pjPZrMhlUr53ve+NyCeAjidTq5evcqhQ4dISEhg1KhR3m7SkJSdnc0vfvEL1q5dy3PPPUdVVRXf+973yMzMHFBjQcKN3TAAFAoFCQkJPP/886hUqi/9wbrHCXQ63YD4wTscDo4cOYLFYqGwsFDshNNHFAoFsbGxPPLII6SkpPDqq6/y61//mqVLl1JQUOCzxVYGmxsGgEqlYuLEiSQlJd1wko/NZqOpqcnrS4GdTidms5n333+fuLg4CgsLB9zkpKFEoVAQFRXFggULCAgIYN26dbz00kvU1NQwZ84cIiMjvf6ZEG7shpdspVJJWlraTU8ihULh2SfAm6xWK1VVVZSXl1NUVCSW/fYDqVSKRqNh3rx5/PznPycuLo6//vWvrF69mtra2gE5QUz4X97vs/cinU7Hhg0biImJYdSoUaLSbT+SSqWMHDmSlStX8thjj7FmzRp+/OMfc/ToUUwmk6gyNEANmQBwuVxotVq2bdvG1KlTSUxM9HaTfFJ4eDjf+MY3WL9+PQqFgp/97Ge8+OKLXL161dtNE77EkAmA9vZ2Dh8+jFar5Z577iE0NNTbTfJJMpmMwMBARo4cyW9/+1vuv/9+9u3bxw9+8AM++ugj2tvbRW9gABkyI2T19fVs3bqVgoICUlNTB1xhEl8ikUjw8/MjJyeHkJAQkpOT2bBhA3/60584deoURUVFZGZmipAeAIZEANhsNk6ePMnVq1f54Q9/KOb9DyAxMTHMmzePcePG8fbbb7N+/XoOHTrEAw88wOTJkwkPD0epVA6IR8i+aEi861qtlrKyMoKCgpg7d66Y9z/A+Pn5kZKSwi9/+Uv+/ve/k5SUxMqVK1mxYgXl5eVikNCLhkQAnDx5kvr6epYtW3bdMmVh4Bk2bBhPP/00q1evJigoiKVLl7Jy5UpOnDgxKDaXHWoG9S2Ay+XCYDDwwQcfEB8fT2FhoTj5Bzg/Pz+USiXjxo3zbDW3c+dOfve73zF8+HCKi4vJzc39ypmnQu8a1AHgcDgoLy/n6tWrLF68WBT8HCTcNQbS09NJSkpixIgR7Ny5k7KyMl566SUmTJhAfn4+qamphISEiNmEfWjQBoDL5cJkMrF+/XoyMzO58847xUq0QcZdcWjYsGGkp6dTV1dHSUkJb731Fh999BEzZ85k1qxZREZGEhgYKAYL+8CgfTdtNhuXLl1i9+7dfO1rXxPTfgc5pVJJZmYmTzzxBJs2baKoqIi1a9cyb948Vq5cSWlpKUajEZfLJaYW96JB2wO4du0ab7zxBoWFhWRnZ4ur/xAhlUqJjIzk0Ucfpbi4mO3bt7N582YeeughsrKyuO+++5g0aRIZGRniZ94LBmUAmEwmLl26xOHDh3n22WeJiooSz/2HCIlE4qlI7O/vz7e+9S3y8/OpqKjg8OHDvPXWW2zcuJFhw4Yxbdo08vLyiIyMFMuPb9GgDIDGxkY++OAD8vLyGD16tPjhD1EKhYKIiAjCw8MZPXo006dP5+jRo+zbt4/y8nJOnDhBRkYG+fn55OTkkJiYSHh4OCqVSvQOumnQBYDVauXo0aOcOXOGX/7ylwN2RyKh90gkElQqFVlZWWRmZrJgwQIuXLjAvn372LRpE/v37ycqKoqRI0dy1113kZeXR1BQECqVCj8/P+RyufiMfIVBFwDNzc0cOHCAlJQUJk+eLEaFfYx7/8Jx48Yxbtw4Hn/8cY4fP86uXbvYv38/a9asIT4+nkmTJjF16lQKCwtJTk72eq2KgWpQvSsul4sPP/yQtrY2nnrqKXHy+zD3FV2lUjF+/HiGDx/O0qVLaW1t5cCBA3zyySf89a9/5ZlnniExMZGioiIKCgpITk4mPj4epVIpegUMogCw2+2cOXOGbdu2UVhYSEZGhrebJAwAUqkUtVqNWq0mLCyMmJgYEhMTmTVrFpcvX6ampobz589TVlbG4cOHUalUhISEkJ2dTW5uLikpKYSFhREaGuqT8wwGRQC4qxO//fbbyOVyioqKCAkJ8XazhAFILpcTERFBREQE2dnZOBwOWlpaaGxs5NSpU1RUVFBTU8PVq1fZu3cvISEhJCUlkZKSQkJCAuHh4YSGhhIUFIRGo8Hf339IjyEMigAwGo0cPXqUTZs28Zvf/IZhw4Z5u0nCICCRSJDL5cTFxREXF8e4ceNwOBx0dnZy6dIlLl68yIkTJzh58iTvvfcearWayMhIYmJiSEtLY/jw4eTl5REREYFSqUQulyOTyb7w38EcDoMiAOrq6nj++ec9gzpiKyrhVslkMkJCQhgzZgyjR4/m61//Og6HA4PBQFVVFWfPnqWyspKTJ0/y/vvv09LSQlRUFJmZmaSmppKcnExiYiIJCQkkJiYSGxuLWq329j/rlg34AGhoaOCf//wnra2tvPjii8TExAzqxBW8TyKRXPcZksvlKBQKxo0bR15eHhaLxfOrra2NyspKLl68SF1dHQcPHsRgMKDX6zGbzbhcLuLi4khLSyM9PZ20tDQiIyPRaDSeWwj3r4E4P2FAB4DRaGT37t3s3buXxx57jPT0dFHqS+gTUqkUlUr1hWIyycnJ5OTkYDAYMJlMdHR00N7eTnt7O1qtlra2Ntrb2+ns7KS8vJzDhw97bj3+9VZBoVCgVqsJDAwkKCiI4OBgwsLCmD59OuHh4V4LhgEbAE6nk88++4ytW7eSkJDA17/+ddRqtbj6C/1KoVAQHBz8pTtMOZ1OrFYrXV1dnl8dHR20trai1Wo9AdHW1oZWq/X0GNw9EJVKRU5ODqGhoSIA/pXD4UCr1fLiiy9is9l48skniYmJ8XazBOE6/9priIyMvOHXOp1OTCbTdWFhNptJTEz06qPHARkARqOR559/nnPnzrFixQrGjx/v7SYJwm2RSqWesYCoqCjPkmapVOrVXu2AC4Dm5mbeeecdPv30U5544gm+9rWviYowwpDgPtEH0m3sgAkAh8NBXV0dGzduZNOmTSxatIiZM2cSFhbm7aYJwpDl9QBwOp0YDAaqq6t59913OXbsGEVFRTz88MMEBwff9uCIe/tyl8vlmczR38xmM3a7HbVa7bXBHofD4XkfNBqNV9oAn78XTqcTuVyOUqn0WjsATzly94rB/uRyuTzzD9RqtdfeC6+MPrhHT/V6PdeuXePjjz/mqaee4vDhwzzwwAP89Kc/7bWRUavVysmTJ9mzZw9dXV290Pqeu3DhAlu3bkWn03mt/r3FYuHgwYN88sknXjm+W2NjIzt37qSlpcWr7QCorKxkz549dHZ29vuxnU4nra2tbNiwgdbW1n4/vptXegB6vd5T4WXbtm20tLSwaNEi7r//fjIzM3t1pZZ7LkFVVZXXtqMqLS1l7dq1jB49mqCgIK+M+nZ2dvLBBx+gUCiYOXNmvx/frbKykrVr1xIWFkZCQoLX2gFw8OBBjh07Rnp6er/fatrtdurr63n++efJysoiPj6+X4/v1i8B4HK56Ozs5MyZM+zdu5eNGzei1+vRaDSMGjWK+++/n5SUFEJCQnp9oo/L5cJut2Oz2bx29bXb7Z7ut7e4XC5sNpvXju/mcDiw2Ww4HA5vNwWbzea1z4XL5cLpdHpuiXqTzWbj4MGDbN++nfb2dlwuF8OGDWPu3LlkZfXOt/QAABQXSURBVGVddwHqlwCor69n9erVtLW10dHRQUJCAkVFReTl5ZGRkUFCQgJyuRy73Y5er+/VYxsMBqxWKzabDZPJ1Ouv3x0WiwWHw4HRaMRgMHhlHMBoNHoCwBvvgZvFYsFms2E2m73aDsCrnwuLxYLRaPSEQG8e3+FwEBcXR0REBLt37+by5cvs3LmTw4cP861vfYvp06cTEhLy+WzFXjvqV5DJZFy9epWysjKioqIoKChg5MiRREREoNPpOH78OMePH++z4+v1eqqqqmhoaGDnzp2cPn26z471VcrLy2lra2Pnzp2cOnXKK7cAOp2Ouro6ZDIZGzZs6Pfju504cYKmpiYOHDjg9XGA06dP09DQwK5du6isrOzXY9tsNi5fvozBYGDfvn00Njb26uu7XC7UajUZGRmcO3eOa9eu0draysmTJ1m2bBkPPvgg0dHRSFx93C99++23efXVV2loaOjLw3wl9/JPm81GcHCwV9YSdHZ2YjAYCA8PR6FQeOU5sN1up729HeCms9b6kl6vx2g0EhAQ4PVirh0dHVitVq98LtwD4a2trURERPT6ikL3UwaTyURnZydWq9Uz/TgpKYnVq1dzxx139H0AmM1mrFar1+6/tVotq1evpqqqil/+8pdkZWX1exvWrFnDO++8w8svv0x6erpXHkU2Nzfz9NNPo1Ao+J//+Z9+P77b9u3bWbNmDcuXL2fSpEleawfAyy+/TGlpKb/4xS/Iycnp12NbLBZOnz7Nd7/7Xf785z9TWFjY669/8eJFnnnmGfbt24fJZCIyMpLZs2fz1FNPeRbW9fkn8ctWWPUnh8PhqQ4bGBjolUpC/v7+KBQKgoKCPPde/c1kMuHn54dCofBqNSV/f3/8/PzQaDRer+rk/lwEBAT0e1vMZjOBgYFIpdJeP77NZqO6uprXX38drVZLeno6sbGxLFmyhGnTphEbG+vpiXp9IpAgCL1LIpEQFhbGAw88gM1mw+VyERMTQ1JS0hceg4sAEIQhRi6Xk5qaSmpq6k2/1idKoEqlUq/WbpNKpV4vLOnecsvbFWnc7RgIC2Lc74e32uIuHCJWA/YhpVJJSkoKAAEBAV5pQ1xcnGcLM2/9sP38/MjKyvL6ysqoqChyc3MHxCKvpKQkurq6vFJjUiaTERQUxIQJE7wyO9Wtz58CeJvdbken02G32wkODvbKgKRWq0Wv1xMZGYlKpfJKCNhsNrRaLQDR0dH9fnw3nU6H2WxGrVZ7tnXzVii2tbV5Hg/3d2FP9yK1pqYmwsLC0Gg0XumNDPkA8LaGhgbKysqoq6tDKpVSUFBATk6O13ojA4HD4eDSpUscOHCAJUuW4OfnNyBuCfqT1Wqlvb2d+vp6XC4XsbGxxMTE9Pstmk+MAXiDe+793r17+ec//0lZWRnvvPMOzzzzDLW1tdjtdm830Ws6OjrYsGED//3f/43JZPLqGglvMJlMXL16lbVr11JWVkZgYKDXJkUN+TEAb3G5XLS0tKBUKvmv//ov4uPjuXTpEt/4xjfYvXs3CQkJXn8O7g0Oh4NPPvmEEydODIgFQf3N5XJRU1PD6tWrCQwMZOnSpV7d50L0APqIRCIhIiKC+fPnexY7xcfHM3nyZBwOh09++AGqqqro6uqiqKjI608kvMFoNPLRRx9x8eJFHn30Uex2u1d7g6IH0EckEskX6hpIpVKMRiNjxozxuTEAd/WbQ4cOMWnSJKqqqrzdJK9oaGigtLSUoKAg3nnnHaqrq4mJiWHx4sXk5ub2+0Ix0QPoQ/968huNRiorK0lKSiIjI8PnNjixWCwcOHCA9PR0YmJikMvlnnESXxoDqK+vp6Ojg+TkZGbNmsXUqVM5cOAAa9eu9SzW6k8iAPqB1Wqlra2NTz75hO9+97tERUV5u0n9yul00tHRwZ49e1AoFNTW1lJXV4fZbObs2bN0dnZ6bbFYf9NqtSiVSoqKihg7diyLFy8mOzubU6dO0dTU1O/tEbcAfczlctHc3MyRI0eYMWMGUVFRnqufrzz6stls1NfXc+LECcrLy4HPn8G3trbyq1/9ilWrVjF27Fif6BW59w10d/XdexLqdDqvVGwSAdDHmpqaqKmpoaCggNDQUMxmM1qtFo1GQ0REhLeb1y+USiWjRo3i3Xff9fzZrl27WLlyJa+//jqJiYlerxDcX1JTU4mPj+fKlSvA5xcInU5HdHS0V3a/EgHQR5xOJ1qtlldeeYXz58+jUqlQKpU4nU6GDx/OkiVLvN3EfiORSPDz87tuBmJUVBRRUVFER0f71ESgyMhIpk2bRklJCfHx8UgkEnQ6HYsXL/bKlGARAH3IbreTnZ1NeHj4dQNdBQUFXq+G420ZGRksW7bMp05+ALVaTUFBAWFhYVy4cIGAgAAeeugh4uLivHILJKYCC4IPE08BBMGHiQAYpNxbqPfn6LF7j4WGhgaMRmOPvtfhcKDX6/v0cZ97spGvzrK8FbKVK1eu9HYjBguHw0F9fT3r169n27ZtXLt2jcjISI4dO8Y//vEPSktLPSu74PMdgTZt2kRDQwOpqam9VgvQarVSXl7Ob3/7W2QyGcnJyX16/+g+oTo7O1mzZg0ffPABw4YN69ZTDIfDQVtbG8ePH+/zAT+n08nx48dRKBQoFAqv1F4cbEQPoIfca9jffvttrl69CkB8fDwnTpxg48aNnquxexPOsrKyPjk5AwIC+Oyzz2hqauqzHoDL5fJM1tHpdDgcDpxOJxUVFeh0um69RkNDAwcPHiQmJsbz3vUVqVRKXFwcu3btora2VvQEukEEQA+4q7hMnz4duVxOfX09CoWC+Ph45s6di1wux2AweK48drudgoIC8vLykMlkdHZ2egpiuBcE6fV6urq6PKXT3d1Yi8Xi+b3ZbPbsLWC321EqlURERJCQkHBdhR/39+p0Os/Oty6XC4vFgtlsxmQyYTAY6OzsvO7ksNvtGAwGurq6PDsZu7czq6ysZN26ddTX1yOTycjNzUWhUFz3PV81nddisVBSUkJraytpaWnIZDJPIQyr1er5uhuVjnfXtrdYLJ4dfNxLiC0WC11dXZ7fS6VSUlNTCQwMpKSkhI6Ojt788Q9Joo/UQ3K5nLS0NEaPHs25c+e4fPky2dnZZGZm0t7eTmVlJbNnz8Zut3P8+HHGjRtHeHg4NTU17Nq1C7PZzNixYxk7dixWq5WdO3diMpkYN24c2dnZ6PV6du/eTWJiIqNGjcJut1NWVkZVVRUhISHMmDHjSzeSdDqd6HQ69uzZQ01NDXl5eUyaNAk/Pz9Onz5NbW0tqampfPbZZ+h0Or75zW8SGhqKVCqlvb2dXbt2YbVaSUtLIzk5GYVCQWtrK8uXL8dsNhMeHk5RUZHneNeuXWPr1q20trYyZ84ckpOTv9Dlrq2t5dy5cyxYsMATVB0dHVRUVJCQkODZo6G0tBSVSkVeXt4XKvPodDqOHTtGSEgIFouF6upq4uPjmT59OmfPnuXIkSPk5OQwadIkT7WnUaNGUVZWxqFDh1iwYEGv/vyHGjEGcIukUimHDh0iPDyc3Nxcdu/eTU1NDVKp1FP/b9u2bUyYMIG6ujr++Mc/Mnv2bLKysnj++edxOByMGDGCc+fOsXr1aqZNm0ZKSgo2m41jx44xefJkLBYLR44cQaVScdddd/Haa69x8eJFz3hCSUkJ6enpDB8+nGvXrvHaa68xa9YsUlNTefXVV6mpqSEiIoJnn32WQ4cOodfrsVgsfPzxx1y9epXhw4fT1tbG+vXrCQgIYMaMGfzlL39h27ZtWK1WRo8ejcPhwGKx8MADD5CamkpTUxMlJSUoFAqUSiVlZWUcPnyYKVOmXHfyulwudu/ezYULF5g+fbpn/cPly5d544030Gg05ObmAvDKK6/Q3NzMyJEjr3sNi8XCRx99xKpVq2hsbMRkMnHp0iU2bdqExWKhoaGBhoYGduzYQVRUFGlpacDnMw8rKio4cOAACxYs8Kl5Bj0lbgFukXt/wz179mA0Grly5QoLFiygpaXFs7BDoVCg0Wjw8/MjPT2dhIQEpFIpLS0t1NbWolarKSwsxGw2U1VVRWdnJy6XC4VCgb+/PxcuXGD37t00NjZy4sQJoqKiPFfzf2U2mzl9+jRXrlzh3LlzXLhwAYlEQkVFBVKplLy8PORyOUVFRcybN4877riDqqoqDAYD1dXVHDt2jNjYWMLCwpg8eTI2m428vDyCg4MJCAhAo9GgVqs9YxkymYwJEyYwf/58vvnNb/Lpp59isVi+8B5VVVXh5+d33Ults9kwGAyYzWbPn7m3C/u/twAymYycnByCgoKIjIykuLiYRYsWERISQkNDA3fffTf33nsvERERHDlyxPN9arUapVJJVVUVHR0dPrPQ6FaIW4BbFBMTQ0ZGBvv37+fUqVPYbDbGjRtHRUUFmzZtQqvVkp+fj0ajITo6mjlz5tDU1MT58+cxGo3Y7XbP+MH06dP55JNPGDVqFFKplJSUFBQKBRUVFbS3t6NSqbDb7YwfP57x48d/oainyWTi/PnznnEDlUrF7Nmz8ff3x9/fn5CQEEJCQoiLiyM6Opq0tDRKS0ux2+2eXZm1Wi0mkwmVSkVQUBChoaFfOYquVquJj48nISGBrq4uWlpavnCSuVwuGhoaCAoKuuXReLlcjr+/P6GhocTExBAZGel5z/z9/T176gUFBV23lFYmk6FSqbDZbOj1eoKDg2/p+L5ABMAtUqvV5Ofns3v3bt58802mTp1KRkYGiYmJvPfee8jlcn73u9+h0Wg4f/48//jHP5g2bRqzZ8/mnXfeAT4/SeRyOQsXLmTVqlXs2rULuVzOsmXLUCqV2O12/Pz8GDNmDKmpqbhcLs+W1v/6HN7hcGC329FoNEydOhV/f3+cTucXvg4+n5f/r0UnkpKSmDhxIh9//DExMTEcOHCAKVOmEBcX5/kal8t13SDf/+1S2+32LwwCuo/zZYN7LpfL82fugU73nzmdzpsWxbhZl97dXplMhlqtFrcANyBuAW7D8OHDSU1NZceOHRQWFhIeHs6oUaMICAhAqVSiVCqRSqUcPnyYiooK7rrrLjQajecDarPZkEqljB8/nuDgYLZv305sbCxBQUFIpVIyMjK4fPky77//vmcUv7S01PP40S0wMJDIyEi2b9/OkSNHMJlMNDU1UVpaisFguOG/wb2N9OLFi/Hz8+Opp55i8eLF19Wpcz8V+Ndue3cMGzYMi8XyhdsDi8WCTqfD6XRiMBi4du0aXV1dnqcKtzs73Waz0dnZiUKh8Ax0Cl9O9ABuQ0xMDIsWLaKtrY24uDjkcjnDhw/nzjvvZPr06Z6R7/DwcAwGAz/96U8ZOXIkRqORzz77jK1bt3LPPfegUqmYP38+u3bt+nzL5v9/xcrPz2fChAm89dZbvPvuuyQnJ/Od73yHkSNHcu3aNTo6OmhsbMRisTB+/HhGjhzJD37wA8LDw0lNTWX58uUoFAquXLniOclUKhWfffYZRqORrq4uOjo62Lx5M+3t7cTFxSGTyQgNDeXee+9l0qRJxMbGcvnyZV5//XWmTZtGc3OzZ8vppqYmqqur8fPzo7m5mbCwsOsWOY0dO5YLFy58oRei0+l44403uHLlCmq1mujoaMrKyvjb3/7GsmXLCAoKAvB04Ts7O2ltbfU8wmxoaMDf3x+j0UhjYyOtra2o1Wra29sJDg5Gq9XS1dXF5MmTfbLuYE+IpwC3QS6XExYWRnZ2NhkZGchkMpRKJRkZGWRmZhIcHOzZqDE9PZ3ExEQKCgoYOXIko0aNoqCgwDM5JjQ0lGHDhl03q0+pVJKenk5WVhZZWVnMnDmT/Px8QkJCMJvNxMbGkpOTQ0JCAlFRUYwcOZK0tDTy8vK4++67yczM9PRE8vPziYuLIyQkBJVKxciRI0lISADAYDAwc+ZMcnJySElJQa1Wc/HiRRITE4mPjyc5OZnhw4czcuRIz9r+xMREwsPDsVgsjBkzhoSEBCIiIjz3++696CsqKlAqleTm5iKRSLh8+TJNTU2e9+HOO+9k7NixpKenM3r0aNLT0z0718Lnsx5TUlLIysrytDctLc2zrt5ut5OYmMiwYcOIj49HpVJx4cIFKioq+PrXv05iYqIXPhmDh1gN2Au6W93ndqoAdefe2H0MuPl9Mnx+hX3vvffQ6XQsWrTIM9jY1NTEmTNnyMvLIzc395Z3rHG5XBw4cIDjx4+zZMkSIiMj2bt3L/v27ePb3/42GRkZ173u7VZJcrlcGAwGNmzYgJ+fH3PmzBEDgDchbgF6QXc/tLfz4e7ufWxPjmGz2WhpaWH79u20tbWRnp6O3W6npaWF3NxcsrOzb2u7KolEQn5+PkFBQezdu5d58+ah1WrRarU4nc4vvO7tDtY5nU7Onz9PVFQUo0ePFid/N4gegA9zl6M6deoUR44cQSKRkJaWxvjx40lMTOyVxTQul8szRbmjowOj0Uh9fT3jx4/v1Qo4/7pS0b3oSAz+3ZwIAB/ncDiwWq2egTqlUolKper1XYTdj/vsdrtnW+zeXq3nDhupVCpO/m4SASAIPkzEpCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPkwEgCD4MBEAguDDRAAIgg8TASAIPuz/ATRis/761rQeAAAAAElFTkSuQmCC)
The distribution of relative intensity I (
) of blackbody radiation from a solid body versus the wavelength
is shown in the figure. If the Wien displacement law constant is
mK, what is the approximate temperature of the object?
![](data:image/png;base64,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)
physics-General
physics-
Five rods of same material and same length are joined as shown. Cross-section of rods ab, ad and bc are A, 2A and 3A respectively. Ends a and c are maintained at temperatures 200°C and 0°C respectively.
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)
If x has the value calculated in above question. Then temperature of junction b or d is:
Five rods of same material and same length are joined as shown. Cross-section of rods ab, ad and bc are A, 2A and 3A respectively. Ends a and c are maintained at temperatures 200°C and 0°C respectively.
![](data:image/png;base64,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)
If x has the value calculated in above question. Then temperature of junction b or d is:
physics-General