Physics-
General
Easy
Question
A ray of light strikes a corner reflector as shown in figure. As the angle of incidence q is increased, the angle between the final reflected ray and the incident ray
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g6dCiUlZVx5coV2Nvb19tmaWmpZCz04sULAO9CS+3atQt6enpYunRpvetgyAcmmBr47rvvcOXKFairq6NFixaIioqqt003NzcYGBjg9OnTkv02FYjFYjbgV2DYX6YGdHR04OTkBFtbW5SUlNTb3pMnT/Df//63yncxAJhYFBw2S1YDvXr1wqhRozBixAicO3cOJSUlaNKkyUfZEgqFWLBgAfz9/dnJZJ8pTDA1MGfOHCgrK0NHRweGhoYfLRYA2LlzJ4YMGYJu3bqhrKyMHZb0GcL6/xqo6AlGjhyJ8+fPf7SdhIQEHD9+HBs2bJCklZSUYM6cOYiMjKy3n4xPAxNMLZkwYQJOnjz50eUXLFiAnTt3Sr1Q1NTUxK5du3DlyhW4uLggOjpaFq4y5AgTTDW8Hy+sc+fOEAgEtdqf/z5HjhyBiYkJhgwZUumelpYW1q9fj23btuHkyZO1iv7PaDjYtPJ7lJeXY8uWLdDX10dSUhI2bNgALS0tjBkzBt27d0dMTAxOnz5d69ms7Oxs2NjYIDQ0FLq6upL0srIyDBgwoNK0skgkYhMCCgzrYd7jyJEjaNWqFRYvXoxJkyZh/fr1AN7FQHNyckJsbKzUAU01sXz5cmzYsEFKLB+CiUWxYYJ5j8uXL0uW1ffs2RMXLlyASCRCjx49YGlpCU9Pz1qfnnzt2jUUFxfju+++k6fLjE8IE8x7PH/+HKmpqXj48CEeP34MFRUVJCYmYsWKFVBRUYGjoyMyMzMRFBT0QTtcLhfu7u7Yu3fvJ/Kc8SlggnmP4uJicDgcKCsrQ1lZGRwOB+Xl5WjWrJkkz/79+7F69WqkpKQgMTGxSjvr16/H/PnzJacjVwWXy4WrqytSUlJk3g6GnGiYndGKS48ePejly5dERCQWi8nAwKDKE8FCQkKoR48e5OPjQ2PGjKHExETJvYcPH5K1tTWJRKJq66nY05+WlkYrV66kVatWUUZGhuwbxJApTDDv4ebmRqdPnyaid2dk2tnZVZv35s2b1KVLFzIyMiJLS0sSiUQkEAioZ8+eFBUV9cF63g+CkZycTEuXLiU/Pz/ZNIQhF9jSmPdwd3eHi4sLOBwOQkJCpMIi/ZOkpCTcuXMHlpaWSE9Px4sXL3DhwgXExMTA3t4enTt3rlO9rVu3xu7du1FaWiqLZjDkBHsPUwUikQjZ2dk1Rm65f/8+li5divj4eDRu3BidO3dGfn4+wsLC0KhRow/WUd17GIZiwwb9VaCsrAxjY+MawxwNGDAAjx8/RmFhITIzMyEWi7F79+4axcL4fGGCkREHDhyAqakpBg0a1NCuMOQIE4wMyMzMxK5du7Bt27Y6leNyufD09ERhYaGcPGPIGiYYGbB06VJs2rQJOjo6dSqnqamJyZMnY/Xq1fj5558/eLwfQzFggqknly5dgkgkgqOj40eVt7CwgL+/P+zt7bF06VIEBATI2EOGTGnoee2q+P777+nt27cN7UaNVAQXT0tLq3PZ99/DVJCVlSUL1xhyQiF7mEGDBsHd3b2h3aiRn376CUuXLkWLFi1kZpMF4FNsFFIwc+bMQVxcnORgI0Xk/v37eP78OebPn9/QrjA+IR8UTF1icMXHx1d6Sx0bG/tR585zOBz4+vrC1dUVfD6/VmUSEhLqNWi+f/8+Dh06hKKiohrzCgQCLF68GH5+fuxIiq+MagUjFArh5+dXa0N//vmn1MrdvLw8jB49utJW3+rgcrlSgjMzM4OTkxO8vb0/WE4sFmPVqlV4+fIlPD098fTp01r7XIG/vz/S0tLg4OCARYsWoays7IP5N27ciAkTJqBTp051ruufFBcXw8fHBwKBoF52GJ+QDw1wSkpKiIhIIBBQWVkZFRQUkFgsJiKisrIyys7OJqFQSERE5eXlklW9IpGIcnJyaPjw4ZK00tJSKigoIKJ3q4C5XC4VFhaSUCik0tJScnZ2rjR4FggEZGVlRc+ePavWx4sXL5KXlxcREXG5XLK2tpb4WBvEYjF16dJFUmbHjh3k4+NTZd7o6GhydHQkDQ0NEggEta6jKioG/Xfu3KGpU6eSv78/lZeX18smQ/5U28PEx8ejX79+4PP5GDt2LLy9vbF48WJs2bIFRIR//etfCA8Px7Bhw1BSUoKJEyfiwYMHyM/Px/LlyxEWFiYJHxQcHIxbt25h0aJF+Ouvv7B69WosX74cXl5emDZtGgoLC5GUlIQbN25I+aCqqoqtW7di4MCB1fZUN2/elJxtXxEzLD4+vtY/GG/evIGmpqbk0ap///5Vbg47ceIEzM3Ncf78eRgaGkJVVbXWdXwIGxsbBAQEwMTEBD/88AOuXr0qE7sM+VDtauUOHTpAV1cXjRo1goWFBUaPHg1TU1PMmDEDERERaNy4Mezt7dGsWTM0atRI8qU9duwYhg4ditGjR6NLly4A3i0bmTRpEnr37o3Y2Fh0794dPB4P8+bNw7fffovmzZujVatWcHBwqOTHsGHD0KFDBzg5OWHlypXo0KEDWrZsKbn/8uVL6OjooKCgAADA5/Px4sULdOzYUcpOfn4+Ll26hFmzZkmlJyQkIC8vDz4+PgCA9PR0JCUlSeXJzc2Fl5cXOnXqhJSUFLmEcx0xYgRGjBiBuLg4mdtmyI4PLu//54CWw+FAVVUVYrEYPB4PL1++BABJFMeKvG/evIGBgQGA/48TnJGRgfHjx0NVVRVZWVkIDg6W5K8p6INYLMb169dhYmKCXr16YceOHbh06ZLkvkAgQP/+/SVruE6fPl2lzcLCQgQGBlYSjKqqKvT19bF48WIAwOPHj3Hnzh2pPHw+H0ePHsXgwYNhb28v12PA3xc6Q7GoVjAikQhFRUXg8/koKCgAl8tFbm4uSktLYWVlhYSEBMycORPt27fH2rVrweVyUVJSgilTpmDWrFngcrnIzMzEixcvYGtri+HDh6NPnz744Ycf8PbtW4hEIpSVlUlO4NLQ0MDhw4exZMkSaGhoSPmxatUqjBgxAtu2bQOXy0VUVJSk92rXrh0EAgG0tbUBAKmpqbC0tKzUnpYtW2Lfvn2V0s3NzSW9EwDExMSgR48elcr27dsXrq6u0NbWlhzcyvgKqW5wk5OTQy9evKD09HSKiYmh169fS/5fXFxMfD6fnjx5QmVlZVReXk4vXryguLg4IiJ68+aNJD/Ru4H1s2fPJIP6V69eUUxMDOXl5VFMTAzl5uZSVlYWJSUlSflw4sQJKi0tpQcPHpCSkhIBIAAUGRkpyRMYGEirV6+W+Ny/f/8qB/2JiYnk4OBQZVvHjx9Pz58/J7FYTM7OzpUmGXx9fally5ZE9G6wLguqe9PPUGwUcmkMERGfzydLS0vJlzc4OJisra0JAP3999+SfGKxmFasWEHbtm2jtWvXUkJCQpX2cnNzydfXl4j+f9aPz+cTEVF2djatW7eOduzYQQ8ePJAq9/btW7KwsKDMzEyZto/H41HHjh3p7NmzdZrVYzQsCiuY6li3bh3NmjWrynsVX7zi4mJas2YNzZo1izZv3kw8Ho9ycnJo+/bt5OHhQaqqqqSrq0vnzp2TKl8hoH/i4uJCBw4cIKJ3U+cXLlyQSTt4PB51796dTp06Rc7OznTlyhWZ2GXIF4UVDI/Ho2PHjlV6N1NSUkKdO3em169fS6WfP3+eSktLJdd37tyhFi1aEACaMWMGhYSEUKtWrQgA6ejo0IIFC+jkyZP0/PlzSZkLFy5IBa9ISEigLl26SOyGh4eTnp4ehYWFyaR9FY9kycnJ5OrqSmvWrKHs7Ox625YHr1+/lrxz+5pRWMHk5ORQp06d6OnTp5XuXb9+nezt7SXX3t7eZGVlRcnJybR+/XoaNmwYtW/fntq1aycZ9zg6OtKUKVNISUmJmjRpQi4uLuTh4UGjRo2i9u3b05IlSyg0NJTU1dXpyJEjRERkZ2dHN2/elNTj7u5OAKhJkyZ07969erWvqjFMfHw8/f777/WyW1v4fD75+flRmzZtqvwB2Lt3L5mZmUk+fwMDA7p27don8U2RUVjBEBENHTq0SsEQEU2dOpVOnDhBycnJBICsra2pb9++tHXrVgoPDycvLy9SVlYmHR0dOnjwICUnJ9Ps2bPp/v375ODgQEOHDqWAgAAiIsrLy6OTJ09S165dqU2bNqSvr0/+/v40c+ZMqTq7detGhoaGZGxsTJMnT65X2xRh0F9YWEiGhoY0ceJEqfSysjKysrKiTp06SdLy8vI+GGfta6FawRQXF9Pjx4/p1q1bJBAIKCwsjC5dukQ8Ho9CQ0Pp9u3bxOfzKSEhQWrWSpZ8SDDZ2dlkbm5OW7duJQCSWTQXFxcqKiqixMRESkxMlCzHSU1NJVdX1yptJSQk0ODBgyW9EQAyNjamvLw8qXwTJ06khQsX0vz582ns2LH1atv7gnn16hXZ2dnRN998Qy4uLsTlcutlvzZwuVxas2YNaWtrU3x8vCTdz8+PtmzZQubm5kT0bpLk7Nmz9OrVKyorK6MTJ05QZGQkbd++nXJzc8nPz49evnxJe/fuJbFYTG/fvqXff/+dfHx8JMEJk5KSKCAggIKDgyk4OFjubZMX1b6HuXbtGnx9fTFs2DAIBAI8evQIAwcOxI8//oiJEydi48aNCAkJQXp6eq0j08sSQ0NDuLu7Y9OmTejVqxfatm2LIUOGYMGCBQDenbvyT3R0dDBu3LgqbbVr1w63b9/GsWPHkJSUhMDAQAwYMAB6enpS+caMGQNbW1tMnDgRd+/ehUAggJqaWr3bsn37dnh4eIDH48HGxgZ6enrYvHlzve1+iCVLlqBp06bQ09PD7NmzsXPnTuzZswdCoRCPHz/GlClTcOzYMQDvFsbu2LEDXl5e0NPTw86dO2Fra4uUlBQMGjQIHh4eWLNmDUJDQ+Hs7IzZs2fj5MmTiI+Px9ChQxEeHo7nz59jw4YNmDNnDvLy8mBnZyfX9smLagXTvXt3tG3bFmvXroVAIEB5eTkiIyPx9u1bDBo0CAYGBoiMjERycjIGDhwoc8eys7MhEAjw8uVLybKb95k5cyYCAgKwdu1a2NraftBeTk4Otm/fXuWhRsC7VQkzZ87E9evXER4eDn9//0p5vv/+e3A4HAgEAgiFQqkXrB9DxUvhXr16oUWLFkhISEBZWRk6d+4MTU3NetmuiX+e1blixQp06dIFGzduRFBQUKXTBnR1ddG6dWsAgL6+PgwMDDBmzBjJ311LSwvTp0/HypUrERAQAH19fTRq1AiWlpYwMjLCqVOnMHDgQGhra+PHH3+Ua7vkTa2Wxly6dAl5eXmYMGECIiIiAACenp6SRZTywMjIqFYbyHx9feHo6IiHDx+icePGH7Tn4eHxQVslJSVwc3OrdgFkxecxYMAAhIaGwt7evkb/PgSHw4Gbmxvatm2L+/fv47fffkNcXBwiIiKwcePGeh1AWxsqjlFv3bo1xo0bhz179uDNmzc4cOAAQkJCPlj2/c+64jo6OlpqrV2HDh2QkZFRZZnPkWpXEb569QpZWVnIy8uDlpYWzp07h5CQECQmJiI1NRWdO3eGhYVFg3et7du3h7OzMzZt2vTBfPn5+Th48OAH83h4eGDu3LmSX9Pq+Pbbb2WyG1RNTU0SAGPNmjXQ09PD0aNH8euvv8pdLABA78awAAA3Nzd4e3tj7Nix4HA4UveqK1vVdZ8+fXDv3j3JdUFBAUaOHFllmc+Sjxn48Hg8Ki0tpVOnTslqLFUvysvLqVevXh/cN5OamkqLFy+u9v7ff/9N/fv3r9VMUGpqKllbW3+UrxVUNUv24MED2rdvX73s1hY+n0+BgYE0d+5cycD8p59+IpFIRAUFBbRp0yYyNTWliIgIysvLo9GjR9OePXsoNTWVBg4cSDt37iQ+n09xcXHUoUMHCgwMJCIioVBICxcupGXLltH58+dp+/btxOfz6fjx49S1a1eKiYn5JO2TFx8lmM2bN9PUqVOlXhQ2NI8ePaIBAwZU+4UvLi6mkJCQKu9VCK4us33m5ub1ar8iTL+2NSoAAAwtSURBVCvLEz6fX+UxIZ87H7WxY926dQgICJA6Qruh6d27N3r37i3Z1/I+OTk51Uam3L59O+zs7NC1a9da19e3b9+POlH5a0FNTe2LjDGtkFFjPpbNmzdj//79SE1NrXTPyMgI69atq5SekJCAkydP4l//+led6pLVOIbxefFFCUZTUxNbt26VbAb7J2/fvsXRo0crpS9YsAC7du2q8wyOLARTXl5e6yAhDMXgixIMADg4OEBdXR2BgYGV7r2/E/Pw4cNo06YNbGxs6lxP+/btkZKSUq8vvEgkwsyZM3Ho0CGIRKKPtsP4hDT0IEoeZGZmkoWFhVS42eLiYrp7967kOisri8zNzSk/P/+j65kyZQrdv3//o8r+c9B/9epVmjJlCgUEBLD1WgrOF9fDAECzZs2wcuVKrFmzRpKWk5ODrVu3Sq6XLVsGT0/Pei3rkdU4xsHBASdOnEDjxo3xn//8p972GHKkoRUrT2xtbSW9SnFxsWRJ/tWrV2nMmDH1tv/8+fNqtz3XxJc+rfyl8kX2MBX4+flh2bJlkjVbAQEB4HK5WLNmDfbu3Vtv+xYWFh8dDpfxefJFC6Zjx45wcnLCzz//DODd0oz169dj/vz5aNWqVb3tczgcdOnSRRKwkPHlo9CCSU9Px9y5c2FnZ1fpV5yI4OTkBBcXF8nivqpwd3fHH3/8gczMTPTq1Qvh4eFYtGiRzHyszzjm/ZkxLpcLb29vdOnSBZmZmZXye3l5YciQIYiLi8PKlSurnCZnyBeFFkyLFi3Qs2dPPHnyBNeuXZO6d/fuXYSEhMDExATGxsbV2lBVVYWPjw8WLFiA1atXw8/PT6aRK+sjGD6fj6lTp0pC02pqasLBwQHp6enYs2ePVN7c3FwcOnQI6urq6NixI1RUVD7JAk2GNBwixV5C6u/vj5SUFNy9exd3796VpC9YsAB8Ph/t27fH+vXrQURVBvCroOIXu3nz5jL1j4iQkJCADh061Lmcvb09tm3bhqNHj+L27dtwcXGBvr4+zpw5g7179yI5OVmyL8bLywtCoRBPnz7FlStXcOTIEfTp0wcWFhYybQ+jBhpwwqFW7N+/n5KTk6lbt26SFbFnz56la9eu0dy5c2nTpk2VysTGxlJQUJBUmqenp9SMVmpqaqWQSb/99pvUdWFhIe3atUsqzc/PTyp6ilgspl69elFoaKgk7dy5c5IghhXs2bNH6vrYsWOUm5srlfb8+XPy8vKis2fP0rx588jNzY2I3m2h9vLyogMHDtDo0aMl9bJ4Zp8ehX4kq4DD4cDd3R3//ve/QUQICgqS7LGoivv376Nv375SaRXB0wEgMjISFy9ehLW1tVQeoVAodf3o0SP0799fKq28vFxqxUBMTAysra2lHsvS09OlHhPfvHlTaY9NdnY29PX1pdIsLS0xfvx4AMCqVavg7++PoqIi+Pj4VBp3cTgcdphTA/BZCAYAJk+ejKysLKxduxb29vYf/LLk5ORIvZDk8XhQV1eHsrIycnNz4erqimfPnsHQ0FCSp6CgoNKYICoqClZWVlJp79f78OFDzJgx44PjmNDQUAwYMEAqraalMKamphg6dCg2bNiAxo0bVxIXo2FQeMEIhUKUl5dDRUUFq1atwoULFzBhwgQA1S9erKqnMDU1xR9//AEDAwO0a9euUpmwsDD07t1bKo2IoKLy/7u4X716VSm6fklJCXr27IlXr15BLBajpKSk0n78/Px8qS98fn5+pSAd77cXgOR9UcViUrZYs+H54J7+hiYnJwf5+fl49uwZjI2NMXv2bLRt2xbKyspISkqS9AgZGRmSR6CioqJKjz8ZGRmYMGGCZFKg4td9xowZ0NPTw88//4w3b95g6NChUuX+2QMB787sfD/YRkVP1rVrV0REREAsFld61GvatKnU9cuXLyv1OMC7aeVnz56hqKgI+fn56N27N44fP44WLVogJycHeXl5aNOmDWJjY2FmZlbzB8iQOQo/SyYrkpKSsGTJEly9ehWzZs2CpqYmFi1ahI0bN8LY2Bg7d+6sl/1du3YBgNyCgjAUA4V/JJMVWlpaUlFe7OzsYG5uju3btyM4OLje9r/99lupaW/Gl8lXI5iKE9TeR1dXVyZbrbt3746oqKgvIzIKo1q+GsEUFRXh8uXLkuuKL/Z///vfSoHrPgYlJSWYmZlJjjJkfJkoe3p6eja0E5+CJk2awMbGBjo6OlBTU8P58+dRVlaG3NxcLFq0SCbvNFJTU5GZmVlpto3x5fBVDvrlxYMHD7B7926cPHlSbnUwGpav5pFMS0sLI0aMkGsdvXr1wuPHj+VaB6Nh+WoEo6SkJPfYvqqqqjAxMUF8fLxc62E0HF+NYDQ1NTFs2DC518PilX3ZfDWCUVNTq3JJjKxhgvmy+WoG/Z8KHo8HKysrREdHN7QrDDnw1fQwnwp1dXXo6+tXGa6W8fnDBCMH7O3tWQ/zhcIeyRiMOsB6GAajDjDByIFHjx4hISEBUVFRMrNZWlqKuLg4mdljfBxMMDXA4/Gwfv16jBo1CsePH4ejoyPCw8Orze/l5QVDQ0PMnTsX06dPr3U9VcUh+yeHDh3C4cOHa22PIR+YYGpAXV0dAwcOhLm5OaZPn46pU6dKHUDL4/GQlZUl+f+tW7dgYGCA27dvS8UVKCgoQEFBAYB325CLioqQm5sLADh48CDOnDkj2VqdlZUFHo8nKZufn49OnTrJva2MmlHoLcqKhEgkQmFhIe7evYvZs2cDeLc1IDc3Fzdv3sTgwYPRoUMH5OXlITQ0VGrdWmBgIHR0dLBv3z54enoiKSkJ6enpiIyMhL29PeLi4sDlcpGbm4vLly+jQ4cO2LJlC06fPo1Tp07BwMAA9+7dg7a2dkM1n/E/mGBqSUJCAhYsWAAHBweMGzcOwLtg52PHjkXXrl2RmpqKSZMmQU9Pr1IIqKNHj+L777/HgAEDEB8fj8OHD+PKlSvIyckBn89HaWkpioqKIBKJcOvWLejq6qJfv36Ii4vDhQsXcOPGDbRq1Qp//PFHQzSd8Q+YYGqJqakpNmzYgGHDhmHQoEH45ptvkJ2dDTs7OzRt2vSD8Z1zc3MxceJEKCkpISMjAz///DPS0tLQsmVLFBUVSfKVlJRATU0NkyZNgpOTE+Li4vD69WuIxWIWg0xBYGOYGhCJRIiJiUF6ejoaNWoEX19fTJ8+Ha9evYKTkxNsbGywcuVKpKSkID8/H2lpaSgoKIBAIEBhYSH4fD66d+8Oe3t7uLm5QSgUYs6cOXBwcICrqyvS0tKgoaGBP//8EyKRCPHx8ZgxYwY8PDzQqlUrdOvWDUuXLsXly5cRGxvLwiw1MOzFZQ3w+XzJDFbTpk2ho6ODzMxM8Pl8tGnTBomJiVBTU0OrVq2QnZ0NHo8HVVVVNGrUCHl5eTA0NETTpk3x4sULtGzZUjIRkJqaCmVlZRgbG0MgECAxMRFmZmYQi8V4+vQpunbtCjU1NYjFYrx8+RKtWrWCmpoaNDQ0GvLj+OphgmEw6gB7JGMw6gATDINRB+o8SyYiQBkCiIQcKP8vzheRGLm5ee8MauiiqboQRXnFECg1ho6eJpR4xUjiaaKdRgGKylTRWFsL6sofqkVxEAgE8PPzg4mJCTIyMmBjY4PQ0FDw+Xw4Oztjx44dGDlyJKytrXHkyBGMHz++XiczMxSbOvcwyhwAHDWJWACAw1GCoaEhDA0NodtEBRylxtAxNIShvhbUOByoaGjjyJmjeFsigq7u5yMWAFBRUUFkZCSKi4vRs2dPHDx4EDNmzEBkZCQSExPRpEkTREREgMPhQE1NjYnlC+eTvYeZM3kaDPTVPlV1MkNJSQmampqwtLSElZUV1NTUcOjQIeTk5EAkEsHV1RVDhgyBjY1Npcj+jC+Peo9h4hOza5Wv3Wcoln9ScSitq6sr5s2bByMjI5SVlaFJkyaYOnUqvL290adPnwb2kiFv6i2YDu2MZOGHwsLn86Grq4vExEQAgKOjIzZs2IDevXtLwilNnz4dY8eObUg3GZ8I9h6mHhARbty4gejoaCxcuBBqap93L8qomfpPK5Ow5jxfKGKxGFevXoWdnR0Ty1cC62EYjDrAXlwyGHWACYbBqANMMAxGHWCCYTDqABMMg1EHmGAYjDrABMNg1AEmGAajDvwf7A1SlNiDjWYAAAAASUVORK5CYII=)
- increases
- decreases
- remains the same
- Information are insufficient to decide
The correct answer is: increases
Related Questions to study
physics-
A ball of mass m is attached to a rigid vertical rod by means of two massless strings with length L. The strings are attached to the rod at points a distance L apart (see Figure). The system is rotating about the axis of the rod, both strings being taut and forming an equilateral triangle. The tension in the upper string is T1
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)
A ball of mass m is attached to a rigid vertical rod by means of two massless strings with length L. The strings are attached to the rod at points a distance L apart (see Figure). The system is rotating about the axis of the rod, both strings being taut and forming an equilateral triangle. The tension in the upper string is T1
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)
physics-General
physics-
Two identical resistors with resistance R are connected in the two circuits drawn. The battery in both circuits is a 12 volt ideal battery. Which statement is correct?
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)
Two identical resistors with resistance R are connected in the two circuits drawn. The battery in both circuits is a 12 volt ideal battery. Which statement is correct?
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ImWeDv74/i4mKxe1ZWVvDw8JBK+TExMQgPD8eSJUuwfPlyqY/2iQhRUVGIjIyEl5cXfHx82r744AM65SDk2bNncHd3R3FxMdauXYvs7GzU19cjNDRU1McbPXo0UlJSUFBQgM2bN6OhoQGrVq2Cubn5Z9draWn50cJYaW6S4vP5sLa2xs6dO1FSUoKwsDCp1vxycnLg8/mYNGkSwsLCUFRUhNDQUOkYXZJ2uiP2Ad8/HUsoFJK+vj4FBAR89FxNTQ1FR0fT8OHDadasWVJZwdFWZL0ts66ujmxsbOjOnTsyi1FTU0MTJ06kkpISqZTXZfqAAoEAAoFAdF1SUoJVq1bBwMAABQUFSE9PR1paGrS1tTlUKVuUlZWhqakp9u8gbVRVVaGmpia1d/B1yib4HS9fvkRRURGSk5Nhbm4OPz8/ZGRkICAgAE+ePMHy5cuRn5//WVMvjNbRqWvAN2/eIDs7G3v27EFoaCh69+6NESNGYNy4cZCTk8PJkyeRkZEh8xciMtpOp64B+/btCxcXF9y4cQPz5s3DqVOnMGjQIISEhGDbtm3IzMxEXFwcVq5ciTlz5sDV1ZXTXXICgQCxsbFSG0E2R01NDY4ePfpRAlmavHvrqTTotDWgQCAQ9UOCgoLw/PlzBAQEiH4uJycHa2trJCUlISIiAidPnoSHhwfu3r3LlWSsXbtWpuYDgClTpkBTU1OmMZydnVu9YepTdMoasKKiAo8fP4aioiKKi4uhp6eH5ORkeHt7IykpCbNnz4aCggIOHz6M0NBQ9O3bF+Hh4e2as5QGc+bM4TR+R6RTJqJboqqqCjt27EBSUpJoYMJlEprRMp22Cf4UV65cQXp6Onr27AlbW1vOX07DaJkuZ0A7Oztcu3YNCQkJyMzMhL6+PtavX//R0nVGx6DLGfAdJiYmiIuLQ05ODlRUVGBubo45c+agoqKCa2mM9+iyBnyHiooKmpqaMHjwYCxcuFCi06YYn48ua0ChUIiEhATY2NhAR0cHmZmZsLe351oW4wO6pAEzMjJgZWWFsrIynDt3DgsXLuz0byfqqnQ5AyYkJMDNzQ1aWlowNzf/7BuQGK2jy+UBgbdzxMePH0d8fDzMzMywfv16riUxPkGXNOD7cHk2DON/0+WaYEbnghmQwSnMgAxOYQZkcAozIINTmAEZnMIMyOAUZkAGp0i0JH/w4MH4+uuvZa1FJnTlfcBdAYlmQl6/ft3247c4Rl5ens0Hd2AkMiCDIStYH5DBKcyADE5hBmRwCjMgg1OYARmcwgzI4BRmQAanMAMyOIUZkMEpzIAMTmEGZHAKMyCDU5gBGZzCDMjgFGZABqcwAzI4hRmQwSnMgAxOYQZkcAozIINT/g/P2/NlLCI4egAAAABJRU5ErkJggg==)
physics-General
physics-
The equivalent resistance between the terminal points A and B in the network shown in figure is
![](data:image/png;base64,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)
The equivalent resistance between the terminal points A and B in the network shown in figure is
![](data:image/png;base64,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)
physics-General
physics-
A hollow conducting sphere of inner radius R and outer radius 2R has resistivity '
' a function of the distance 'r' from the centre of the sphere:
. The inner and outer surfaces are painted with a perfectly conducting 'paint' and a potential difference
is applied between the two surfaces. Then, as 'r' increases from R to 2R, the electric field inside the sphere
A hollow conducting sphere of inner radius R and outer radius 2R has resistivity '
' a function of the distance 'r' from the centre of the sphere:
. The inner and outer surfaces are painted with a perfectly conducting 'paint' and a potential difference
is applied between the two surfaces. Then, as 'r' increases from R to 2R, the electric field inside the sphere
physics-General
physics-
If I = 80 mA, determine the magnitude of the current in the
resistor
![](data:image/png;base64,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)
If I = 80 mA, determine the magnitude of the current in the
resistor
![](data:image/png;base64,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)
physics-General
physics-
Four wires A, B, C and D are made of different materials. They each carry the same current I. Wire B has twice the length of other wires. Wire C has twice the internal electric field of other wires. Wire D has twice the diameter of other wires. Other than these differences, all wires share identical characteristics. Rank the conductivities of these materials, from greatest to least
![](data:image/png;base64,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)
Four wires A, B, C and D are made of different materials. They each carry the same current I. Wire B has twice the length of other wires. Wire C has twice the internal electric field of other wires. Wire D has twice the diameter of other wires. Other than these differences, all wires share identical characteristics. Rank the conductivities of these materials, from greatest to least
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAABgCAYAAADhA7tVAAAMl0lEQVR4nO3cf0zU9R8H8CfH4XHcwSEcRVc6RRQzUhppajZqzdhkKU0haq7BaHDmMNhyrbEIpzNY5GY5p+Coxmrp2KoZ0A8iFkMbHESgkWTAHed118Hd0d3p/X73R/O+AYly937fqd/3Y7s/+HD3fr3E5+7zvvfn/bkIQggBxzEiCHcD3N2NB4xjigeMY4oHjGOKB4xjShjuBm4nPp8Pdrvd/3N0dDSioqLC2NGdj7+D/YvP54NKpYJMJsP7778Ph8MR7pbueBF8HWyu2NhYdHR0YP369eFu5Y7H38FuICIiItwt3BV4wDimeMA4pnjAOKZ4wDimeMBmsVgsuHr1Krxeb7hbuSvwgP2L2+3Gzz//jM8//xxWqxVmszncLYXM2NgYdu/eDbFYDKlUiqKiIoyMjAQ97px1sJKSErS2tgY9MHdncrlcMJlM8Hq9EAgEeP7553HixAnExcUFNN6cgPl8PvC11/9PHR0dOHjwILq6uiCRSFBcXIzy8nIsX7484DH5Sj4HABgfH8e5c+cAAEKhEFu3bsXixYuDHpcHjGOKT/I5pnjAOKZ4wDimeMA4pqjtaL18+TJiYmKgUChoDRmQX3/9FT/88AMAICoqCmKxGJmZmVi5cmVY+5rN4XDgs88+g0AggMFgwMqVKxEdHY2nnnqKWo0LFy7gm2++AQDIZDJ4PB6kpKQgKysLUVFRodmSRCgpLS0lVVVVtIYLSn5+PikuLiZer5cMDw+TjRs3kldeeYX4fL5wt0YIIUStVpP169eT8+fPE0II8fl85OjRo6SgoIB6rdzcXKJUKonP5yM2m40cOXKEpKWl+WuzRuUUOTk5ic7OTjQ0NMDtdtMYMij33HMPoqOjIRAIsHr1atTU1OD48eMYGhoKd2sAAKVSiaysLGzcuBHAP5sby8rKkJ6eTr1WQkICYmNjERERAYlEgoqKChQWFqKgoADXrl2jXm82KgFraGjA6dOn4fF48MUXX9AYkiqTyYRFixZBLpeHuxXo9Xq0tbXhmWeemXH8eshCobCwEGq1Gm1tbcxrBR0wp9MJrVaLdevWQalU4vjx4zT6Ctrg4CA++eQTvPHGGygrK0NjY2PY54cA8NNPPwEAVqxYMed3gV7vW6jk5GTI5XL88ssvzGsFPcn/9NNPsWLFCnR1dSE9PR0HDx7E8PAwHnzwQRr9BWzt2rV48cUX4fF4oFAosGfPHixbtgyPP/54WPsSi8UAENY7ljweD+x2O2JiYpjXCuodjBCCnp4e5OXlYdmyZdi0aRNyc3Nx4sQJWv0FTSgUoqysDMuXL8epU6fC3Q4yMjIgFosxODg453dutzskGw36+vpw7do1ZGdnM68VVMA6Ozvx2GOPYcmSJf5HQUEBPvzwQ1itVlo9LtjszYJmsxnj4+O3xW1o8fHxeO2111BXVzdjku1wOPDee+9Rr+fz+Wb8PD09jZKSElRUVOChhx6iXm+2gE+ROp0ODQ0NePbZZ+F2u/13QHs8HiQmJqK2thavv/46YmNjqTV7Ky5fvoyJiQkIBAKcOnUKkZGROHfuHKqqqqBUKkPay40cOHAACQkJ2LRpE7Kzs5GUlIT4+Hjs3buX6trU8PAwfvvtN+j1epw8eRIWiwXj4+OorKxEXl4etTrz4bspwogQgunpaUgkkrv2Kwp4wO4wZ86cQVJSEqRSaUjqaTQapKenIy0tLaDX84DdQSwWC1JSUiCVSrF06VLm9QghuHDhAlJTU9HX1xfQGDMCptPpUF5ejri4OERGRlJrdD5utxs6ne62WARdKK/XC71eD6fTieTk5JDUdDgcGBgYwMmTJ5nX+vPPP1FdXQ273Q6TyRTQGDMm+e+88w6mpqZw33334emnn6bS5HzUajXq6+thMplw6NAh5vVoU6lU0Gg0MBqN2LVrV0hqnj59GhaLBU6nEyKRiGktvV6PhIQEuFwu2O12SCSSBY8xI2A9PT3Ytm0bbDYbtm/fTq3RG2lsbMTmzZvR3NwckjUZ2np6erBlyxY0NTUhKysrJDVbW1shEolgNBrxwAMPMK1lNpuxZMkSuFwuGAwGpKSkLHiMGetg9957LxQKRUg/0SgUCqSmpsLlcoWsJi3Xr2+G+vQuEolCcmOwVCqFSCSCQqEIeAF4RsDcbjdUKhUWLVpEpcGbkcvl6O3txejoaMhq0hQbG4v+/v6QX/ax2+1U7vi5mZiYGGi1Wmg0moBPxzNOkTt37kRNTQ0yMjLw6quvUmlyPi6XCxcvXkRiYiLefPNN5vVos1gs6O/vR1RUFOrq6kJWEwjNhXG5XA6DwYC//vor4A8xMwJWWFiIhISEkO7pWrp0KZKTk0O2k4C2VatWITU1FfHx8cxrjY+P4+uvvw7JJR4ASExMxOTkJKRSKYTCwC768HWwO4jb7UZaWhrMZnPIphRerxdPPvkkmpubA3o99YC1traiu7sbAJCUlISioiLIZDKaJYLS2dmJb7/9FsA/+9SLioqQlJQU5q7+Z2xsDB999BHcbjeEQiF27dqFhx9+mHqdK1euoLGxEQ6HAwKBALm5ucjMzKRe56YBa2pqwtTU1IIGHRoaQktLCwwGAyQSCfbt24eKigom/5HNzc3QarULes2lS5fQ0tKCiYkJiEQiKJVK7N+/H/fffz/1/np6evy35N8qo9GI1tZWDAwMAAB27NiBysrKeXeDDA4OoqOjY0F1zGYz2traoFKpQAhBdnY2Kisr8cQTTyxonPlEVldXV8/3BJVKBavVCq/Xe8sPqVQKp9OJsbExuFwu6PV6JCcnIyMjg1rj1w0MDPi/DeZWHxKJBG63G6Ojo/4rCYmJidiwYQP1/tRqNUZHRxfUn0gkgkAggEajgcPhgFarRWRkJLZs2XLDT3M6nQ4jIyMLqhMVFQWhUIiJiQlcvXoVV65cAQBs3ryZ2mbEgE6R830DT3t7O44cOYLJyUnI5XLs2bMH27dvh0AQulsw5+vv/PnzqK2thU6ng0wmw8svv4z8/PyAJ7EL5XA4IBKJ/NtyZveqVqtx+PBh/6fT5557DqWlpQEtSxBC5uwHu06v16O2thbd3d0QCATIycnB3r17qZ9lAgqYWq1GcXEx7HY7ysvL/Q23t7fj7NmzVBsMxB9//IF9+/bh4sWLeOuttwD8c+dTc3Mzvv/++7D0ND09jZdeegnDw8OwWq04duwYdu7ciYmJCZSUlMBoNGL//v0AAIPBgK+++iro72mz2+34+OOPUVpaivr6esTFxcHpdOLMmTOorq7Go48+SuOfNr9A73erqqoi+fn5M459+eWXgQ5H3bFjx0hWVtaMY+Hs74MPPiCXLl0ihBDS1NREZDIZcTqdhBBCDh06RHbs2DHj+S0tLVTqGgwGAoAYjUb/Ma1WS/r7+6mMfzMBn7dm77y0WCzIyckJNu/UzO7PZrOF9XrnCy+8gFWrVgEAdu/eDalUiunpaQBzezWbzdi2bRuVuv+1Q1YikeCRRx6hMv7NBDUxMplM6OvrQ29vL95++21aPVFjtVrR19cHlUqFmpoaOJ3OsPXy78m5xWJBZmbmjPmOxWLx/y0PHz5Mvf7AwAD6+vpw9uxZfPfdd9THv5GgZraRkZEQi8Vwu923xR3dswkEAojFYni93tuqv/r6+jnbk6736vF4mPQqFov9t8x5PB7q499IUAGTyWRYs2YNAPgn07cTiUTi76+qqor5/qlb0dvbi/T09DmLp3Fxcf5eDxw4QL1uWloa5HI51qxZ4z81hwK1tQOZTAaLxYLe3l5aQ1IlkUjg8XjQ1dUVth5GRkZgs9n886vrF65nk8lksFqt+PHHH5n0IZPJ0N7ezmTs2QJ6ByOEYGpqCpOTk9BoNBAIBDCZTKirq0N9fT3tHgPqz2Qy+W/TEgqFsFgsOHr0aNjmikNDQygvL8fq1avR3NwMm82GnJwc5OXlwWQyYWpqasbf8t1336XyNQzXr8KMjIzA4XDA4XCgq6srZOuSAa2DjY2NQaPRzDm+ePFirF27lkpjwdBqtfj999/nHJdKpUyut92K7u7uOfvat27dCr1eD7VaPef58fHxWLduXVA17XY7BgYG/nPOtWHDBv+cjCW+m4Jjin+FJscUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjHFA8YxxQPGMcUDxjH1N+Ju4kqdG4mTQAAAABJRU5ErkJggg==)
physics-General
physics-
A hollow cylinder with inner radius R, outer radius 2R mass M is rolling with speed of its axis v. Its kinetic energy is
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)
A hollow cylinder with inner radius R, outer radius 2R mass M is rolling with speed of its axis v. Its kinetic energy is
![](data:image/png;base64,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)
physics-General
physics-
Four identical bulbs each rated 100 watts, 220 volts are connected across a battery as shown. The power consumed by them is:
![](data:image/png;base64,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)
Four identical bulbs each rated 100 watts, 220 volts are connected across a battery as shown. The power consumed by them is:
![](data:image/png;base64,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)
physics-General
physics-
Resistors R1 and R2 have an equivalent resistance of 6 ohms when connected in the circuit shown below. The resistance of R1 could be
![](data:image/png;base64,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)
Resistors R1 and R2 have an equivalent resistance of 6 ohms when connected in the circuit shown below. The resistance of R1 could be
![](data:image/png;base64,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)
physics-General
physics-
In the two circuits shown, all the light bulbs and batteries are identical. If A, B and C respectively denotes the brightness of light bulbs A, B & C then
![](data:image/png;base64,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)
In the two circuits shown, all the light bulbs and batteries are identical. If A, B and C respectively denotes the brightness of light bulbs A, B & C then
![](data:image/png;base64,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)
physics-General
physics-
Two strings support a uniform rod as shown. String at end B is cut. Which of the following is true just after cut
I] initial acceleration of A is vertical
II] initial acceleration of A is horizontal
III] initial acceleration of centre of mass of rod is vertical
IV] initial acceleration of centre of mass of rod is horizontal
![](data:image/png;base64,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)
Two strings support a uniform rod as shown. String at end B is cut. Which of the following is true just after cut
I] initial acceleration of A is vertical
II] initial acceleration of A is horizontal
III] initial acceleration of centre of mass of rod is vertical
IV] initial acceleration of centre of mass of rod is horizontal
![](data:image/png;base64,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)
physics-General
physics-
The potential of point O in the steady state circuit shown on the right is
![](data:image/png;base64,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)
The potential of point O in the steady state circuit shown on the right is
![](data:image/png;base64,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)
physics-General
physics-
A mass is at the center of a square, with four masses at the corners as shown.
![](data:image/png;base64,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)
Rank the choices according to the magnitude of the gravitational force on the center mass.
A mass is at the center of a square, with four masses at the corners as shown.
![](data:image/png;base64,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)
Rank the choices according to the magnitude of the gravitational force on the center mass.
physics-General
physics-
In the figure shown the electric potential energy of the system is (q is at the centre of the conducting neutral spherical shell of inner radius a and outer radius b)
![](data:image/png;base64,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)
In the figure shown the electric potential energy of the system is (q is at the centre of the conducting neutral spherical shell of inner radius a and outer radius b)
![](data:image/png;base64,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)
physics-General
physics-
The diagram shows three concentric conducting spherical shells having radii T, 2R and 3R. The initial potential of each shell is as mentioned in the figure. If the inner most shell is earth then the charge present on its outer surface would be equal to
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)
The diagram shows three concentric conducting spherical shells having radii T, 2R and 3R. The initial potential of each shell is as mentioned in the figure. If the inner most shell is earth then the charge present on its outer surface would be equal to
![](data:image/png;base64,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)
physics-General