Physics-
General
Easy
Question
A light semi cylindrical gate of radius R is piovted at its mid point O, of the diameter as shown in the figure holding liquid of density r. The force F required to prevent the rotation of the gate is equal to
![](data:image/png;base64,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)
(B)
- none of these
The correct answer is: none of these
Related Questions to study
physics-
In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2r and 3r. The height ‘h’ for the equilibrium of cylinder must be
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)
In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2r and 3r. The height ‘h’ for the equilibrium of cylinder must be
![](data:image/png;base64,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)
physics-General
physics-
A liquid of mass 1 kg is filled in a flask as shown in figure. The force exerted by the flask on the liquid is (g = 10 m/s2)[Neglect atmospheric pressure]:
![](data:image/png;base64,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)
A liquid of mass 1 kg is filled in a flask as shown in figure. The force exerted by the flask on the liquid is (g = 10 m/s2)[Neglect atmospheric pressure]:
![](data:image/png;base64,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)
physics-General
physics-
An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water spilled out. The acceleration was
An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its side it was found that one third of volume of water spilled out. The acceleration was
physics-General
physics-
Figure shows a three arm tube in which a liquid is filled upto levels of height l. It is now rotated at an angular frequency w about an axis passing through arm B. The angular frequency w at which level of liquid in arm B becomes zero.
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)
Figure shows a three arm tube in which a liquid is filled upto levels of height l. It is now rotated at an angular frequency w about an axis passing through arm B. The angular frequency w at which level of liquid in arm B becomes zero.
![](data:image/png;base64,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)
physics-General
physics-
A fluid container is containing a liquid of density r is accelerating upward with acceleration a along the inclined place of inclination a as shown. Then the angle of inclination q of free surface is :
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)
A fluid container is containing a liquid of density r is accelerating upward with acceleration a along the inclined place of inclination a as shown. Then the angle of inclination q of free surface is :
![](data:image/png;base64,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)
physics-General
physics-
The area of cross-section of the wider tube shown in figure is 800 cm2 If a mass of 12 kg is placed on the massless piston, the difference in heights h in the level of water in the two tubes is :
![](data:image/png;base64,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)
The area of cross-section of the wider tube shown in figure is 800 cm2 If a mass of 12 kg is placed on the massless piston, the difference in heights h in the level of water in the two tubes is :
![](data:image/png;base64,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)
physics-General
physics-
A cone of radius R and height H, is hanging inside a liquid of density r by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the cone is
![](data:image/png;base64,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)
A cone of radius R and height H, is hanging inside a liquid of density r by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the cone is
![](data:image/png;base64,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)
physics-General
physics-
The figure shows a radiant energy spectrum graph for a black body at a temperature T
![](data:image/png;base64,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)
Identify the graph which correctly represents the spectral intensity versus wavelength graph at two temperatures T' and T (T < T')
The figure shows a radiant energy spectrum graph for a black body at a temperature T
![](data:image/png;base64,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)
Identify the graph which correctly represents the spectral intensity versus wavelength graph at two temperatures T' and T (T < T')
physics-General
physics-
Two bodies P and Q have thermal emissivity’s of
and
respectively. Surface areas of these bodies are same and the total radiant power is also emitted at the same rate. If temperature of P is qP kelvin then temperature of Q i.e.
is
Two bodies P and Q have thermal emissivity’s of
and
respectively. Surface areas of these bodies are same and the total radiant power is also emitted at the same rate. If temperature of P is qP kelvin then temperature of Q i.e.
is
physics-General
physics-
The spectral emissive power
for a body at temperature T1 is plotted against the wavelength and area under the curve is found to be A. At a different temperature T2 the area is found to be 9A. Then
=
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)
The spectral emissive power
for a body at temperature T1 is plotted against the wavelength and area under the curve is found to be A. At a different temperature T2 the area is found to be 9A. Then
=
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KEO0UnSlbe9WkWLlzINDQ0uLWFZs+eLfV8fn4+s7CwYGpqakxdXZ0BYB4eHuVtljFWsdfDGjNmDPfeZs2aJXQ5lV5aWhqzsrLi/k4mTpwodEmVUrl7WCtXrsT169c/u5LCnj170KJFCyQkJCAlJQXjx4+Ht7c3zW35An9/f+zbtw8AYG5ujpUrVwpcEalRowZOnz7N9Rx37txJp+gC4OWUsF27dqhXr16Jz127dg07d+6EoaEhatSogZ07d3KDmaS49PR07uZbNTU17N69G9WqVRO4Ktl4e3vD2dkZzs7OFXKGuLm5Oby9vaGpqQkAmDVrFnx9fQWuqnJR+FXCH374QWrHFjU1NYwZMwbXr19XdNOiNH/+fERHRwMAxo8fjx49eghckeyioqJw5swZnDlzRiX2JVSEbt26Yfv27QAKN/0YOnQorl69KnBVlYfCA6ukBeW++eYb3Lx5U9FNi87Vq1exdetWAECDBg2wbt06gSsiJRk7diyWLVsG4H+7a9N0B+WQO7ASExNx8+ZNuS7xWlhYIDExEe/evZO3+QonOzsbY8eO5aZ97NixA7Vq1RK4KvI5S5cu5VbNSElJgYODA6KiogSuquIrU2AVFBRg9erVMDc3R9u2bdG/f38YGxtza4rLKiQkBImJibh27VqZvq8iW7p0KZ4+fQoAcHNzQ79+/QSuiJRm48aN+P777wEULi3eo0cPCi0Fk3kj1by8PIwcORLHjh3DqlWr8PPPPyMrKwuXL1/GyJEjy7SsctFW4UFBQXBxcSl71RXMnTt3sGHDBgBAvXr1sHnzZoErko+lpSVGjBgBQL71sPLy8pCUlISkpCQkJycjKSkJqamp0NPTg7GxMYyNjVVqflfRRZEPHz7g1KlTePXqFbp3745Lly6hadOmQpdXMck6/2H27NkMAHNxcSn23PLlyz87D+tToaGh3Gvt7OzKPA/jYxVhHlZubi5r1aoV9z68vLyELkkp7t69yzw9PVnHjh1ZgwYNWPXq1bnP4EsPLS0t1rBhQ9ahQwfm4uLCJk2axPbt28cSEhIEey8ZGRmsffv2XI3169dnT58+FayeikymwHr+/DmrUqUKU1NTY3fv3i32fGJiIqtZs6ZMgTV48GAGgNWuXZvp6Oiw9PR0+SpnFSOwPg77gQMHCl2OwmRnZzM/Pz82efJk1rBhQ5nCqSwPNTU1ZmtryxYtWsSuXbvGJBKJUt/fmzdvmJmZmdTO20+ePFFqDZWBTKeEV65cgUQigZWVFdq0aVPseX19fZiYmODJkydfPM7Dhw/h7e0NoHAOi5+fH27duiWqS/d8io2NxapVqwAAenp62LZtm8AVlc+JEydw8OBBAMC6devQtGlTeHt74+jRo7hw4QLS09OLfY+GhgasrKygr6+POnXqcI+UlBTs2bMHampqcHV1RdOmTREfH4+4uDju8fEFH8YY7t69i7t372LlypUwMDCAg4MDHB0d4eTkpPALGPXq1cPZs2fRuXNnJCUlIT4+Hj169MDly5fRrFkzhbZdqciSav369WMAmKOj42dfY2FhUWoPa9iwYQwAq1WrFktKSmLz5s1jy5cvL3PKFhF7D8vDw4Orf/fu3UKXU25r1qzh3s+aNWuYtbV1ib2hqlWrMmdnZ3bgwAH24cOHEo91+fJl7vW///57ia/Jyspi9+/fZ7/++iuzs7NjampqJbanp6fHli9fzlJSUhT59hljjAUGBrJq1apJnR4+e/ZM4e1WFjIFlo6ODgPA+vXr99nXlBZY4eHh3A/UokWLGGOMnT9/nvXq1UuOsguJObBCQ0O5eyttbW2VfgqjCB8H1qePWrVqseHDhzMvLy+ZhgFkCaxPxcfHs507dzJHR0emra1drIY6deqwFStWsNTU1PK+1S+6efMmq1u3LtdugwYNWGRkpELbrCxkCqyqVasyAKxLly6ffU1pgeXm5sYAsBo1arDExETGWOENpXp6eiwvL0+O0sUdWN988w1Xe2BgoNDllNuFCxeYqalpsZCwtbVlx44dY9nZ2WU6njyB9bG0tDTm7e3N+vfvX6znVadOHbZy5UqFBldkZCRr2rQp12bDhg0ptHhQph5WtWrVPtut/lJgPX36lOtNzJ07V+q5Tp06sZs3b8pRungD6+zZs1zdrq6uQpdTLqGhoezrr78uFlStWrVifn5+ch+3vIH1sYcPHzIPDw+mqalZLLh++eUXhQXXu3fvmJ2dHdeeoaEhu337tkLaqixkCqwRI0ZwH/qngVPkS4H1/fffMwBMR0eHvXnzRuq5GTNmsMWLF0t97dChQ+zx48el1iXGwMrPz+fGdrS1tdmLFy+ELkkuBQUFbOPGjUxLS0sqBAwNDVnPnj3L3ZtISEhg+/fvZ/v375fpZ0EWMTEx7Icffig2haJu3boKm06SkZHBnJ2dubaqV6/Ozp49q5C2KgOZAsvPz0/qt9Knc17i4+OZvr5+iYFVNCUCKHldpwMHDjAjIyOWkZHBfW3w4MHs0aNHpdYlxsDavXs3V/O8efOELkcub9++ZY6OjlL/6B0cHOTuKSvb+/fv2bJly7if2aLHsGHDuOEKPuXn57MJEyZw7WhoaLA9e/bw3g4fEhMTmY2NjdyPadOmKbQ+mQIrPz+fde/enfvAa9SowRYuXMiuXLnCfv/9d/bVV18xY2NjBoA1a9aMbdq0iZuDMn78eK43ER8fX+zYz58/ZxoaGqxFixZszpw5rF+/fszExESmQWixBVZ6ejr3ORkZGbG0tDShSyozf39/ZmRkJHXFb9u2bby3k5yczIKCglhQUBCLi4vj/fiMFfZ+Fi5cyP1CLfp7OXXqlELa8/T0lArIJUuWKKSd8nj27BkDwJycnNi2bdu4v4OgoCDWrVs3rvaPv753717m7u7OtLW1Wbdu3RRan8wz3d+9e8c6depU4pWXU6dOcaeETZs2ZZs2bWLJycksOjqaGzeYOnXqZ4+9aNEiqWN+eor4OWILrGXLlnH17t27V+hyyiQ3N5fNnTtXagDb2tqaPXjwgHvNiRMn2MCBA9nAgQPLPdObzzGs0ty8eZO1aNFC6mfQw8ODJScn897W7t27pQJy7NixLD8/n/d25HXnzh3Wpk2bEi+SFE36BkqOjRUrVrDWrVsrtL4yLZFcUFDAzp8/zzw8PNj48ePZgQMHuEH4RYsWMT8/P6me0ZMnT9iRI0fYkSNH2OvXr7943HPnzjEPDw/2119/sYKCApnqEVNgJSQkcGMnYpvGEBUVxTp06CD1D3rKlCksKytL6nUfT2u4detWudpUZmAxVjin68cff+QuDhVNRzh//jzvbZ05c0ZqrpaTk5PUkIiQAgIC2ObNm0t8rrTAev/+PbOwsFBkeWULLFUjpsAqOjUGwK5cuSJ0OTI7d+4cq1WrFle7vr4+8/HxKfG1Yg6sIkFBQczc3FwqnCdMmMB7oFy/fp0ZGBhwbdjZ2bF3797x2oY8bt26xSIiIkp8rrTAYoyxOXPmKKo0xhgPa7qT0j1+/Jhbo93V1RVdu3YVuCLZ7Nq1C05OTtz6+z169EBYWFiFXmHD3t4eYWFhmDJlCtTU1AAUfg4dO3ZEZGQkb+107NgRwcHBMDMzAwDcvHkTXbp0wcuXL3lrQx7t27fndryWx9q1a3mspjgKLCWYO3cuJBIJtLW1RbGKKGMMP//8MyZOnMhtZzV37lxcvHgR9evXF7g6xatevTq2bt0Kf39/NGzYEEDhVnXt27fndQ335s2b4/r169yqvE+fPkWnTp1w584d3tqocBTaf1MwMZwS/vfff1yN8+fPF7qcUmVlZbEhQ4ZInRKtXbtWpu/19fVlHh4ezMPDg0VFRZWrjuzsbBYXF8fi4uLKtaJHeSUmJrJevXpxn4WamhpbvHgxr2OQaWlpzMHBQerK66FDh3g7Pl9kOSVUNAosBSooKGC2traimcbw6ZVgdXX1CnFTdnlJJBI2f/58qSukffv2/eyN2/LIy8tjo0ePlvpF8eOPP6rUFUQKrHJS9cA6evSoaKYxPHnyRGqwWUtLix07dkywepKTk1lwcDALDg4ucf6eEE6ePCl1AaJJkybs3r17vLaxfv16qWkP3377LXv//j2vbciLAqucVDmwJBIJs7S0ZEDhfXWqPI3hypUrrE6dOtxnWb16dXbhwoUyH+f48ePMycmJOTk5lXvxOqGuEpYmIiJCagdoHR0ddvDgQV7bOH/+PNPT0+PaMDMzY/fv3+e1DXmoQmDRoLuC/PPPPwgPDwcALFmyBOrqqvlRBwYGolevXtxieHp6erh48SJ69epV5mNFRUXB19cXvr6+SElJ4btUlWBhYYGbN29iyJAhAAq3+fLw8MD06dMhkUh4aaN37964ffs2WrZsCQB48eIFOnXqhMOHD/NyfGVhjOH06dNo37496tevD2tra+zdu7dcn5Nq/isSuYKCAm6jjVatWmHQoEECV1Syx48fY8CAAdwGIsbGxrhy5Qo6duwocGWqrUaNGvDy8sK6detQpUoVAMAff/wBV1dXZGdn89KGubk5bty4gQEDBgAAMjIy4O7ujkmTJpVpwxcheXh4YMCAAcjLy0OzZs0QGRmJcePGoVGjRoiIiJDrmBRYCvBp76poPo8qiY+PR9++fbkdmk1MTBAUFARra2uBKxOPn376Cf7+/jAwMAAA+Pj4oE+fPrz1LmvUqIETJ05gxYoVXA99586d6NSpE54/f85LG4ry+PFjhISE4OXLl7h37x4uX76M27dvw8LCAnFxcRg9erRcx6XA4pkYelepqalwdHRETEwMgMI1+S9cuABzc3OBKxOfonXbjYyMABSeYnfr1g2vX7/m5fhqampYtGgR/P39YWhoCAAIDQ2Fra0tTp48yUsbinDr1i1cunQJpqam3NdsbGxw6NAhAIUTZeXaSFmw0TMeqOKg+5EjR7iajh8/LnQ5xeTm5rJvv/2Wq7FmzZrlvo2myJkzZ5ibmxtzc3PjZR7Wq1ev2KtXr1R+OghjhVdZ69evL3UFke8VRuPj44stljh9+nSlzVMry6D7p/eZfszW1papqanJtZQPBRaPPr0yKOtN3Mrk7u4uNUHx0qVLQpdUYURFRbFGjRpxn6+RkRELDQ3ltY38/Hw2b948qTlhZmZm7OLFi7y2U5JBgwZxbcr7sy2RSFjDhg3ZkCFD5Pp+CiweqXrvasGCBVx9Ghoa7MyZM0KX9FnJycns2rVr7Nq1ayozD0sWL1++lJrPpquryy5fvsx7O76+vlLrkuH/l6pRxJI4RYp+GQNgYWFhch3jwYMHrGrVqp+9wbo0FFg8+bh31bp1a5XrXe3YsUNqBvuRI0d4b8Pb25s5OzszZ2dnUa2HxbfY2FhufbiinuzJkyd5b+fDhw/FZsebmJh8djUNeaWnp7PTp09LrYm/bt06ubZNmzNnzmeXWZcFBRZPPu5deXt7C1rLp06fPi01e3rHjh0KaaciLC/Dl4SEBNayZUvuPVSpUkVhyyKfO3dO6lQUABsyZAiLjY0t97GPHTvGJk+ezMaMGVPsMWnSpDIt833//n1maWlZrluaKLB4oMq9q0ePHklturBmzRqFtUWBJe3du3fsq6++4t5Ho0aN5LqDQBZpaWls6tSpUmNb1atXZ7/++ivLyclRSJtlERMTw+zs7OQ+lSxC0xp4oKrzrrKysjB06FBkZGQAAH7++WfMnTtX4KoqDwMDAwQEBKBdu3bo3LkzEhMT4erqihs3bvDeVo0aNfDHH3/gypUr+OqrrwAUTjZdsGABrK2t4efnx3ubsvrw4QMcHBywfv16tGrVqlzHosAqp4/nXbVu3RoDBw4UuKL/mT59Oh49egSg8HaPVatWCVxR5aOnp4eAgADY2dkhIyMDqampcHBwwL179xTSnr29Pe7evYuDBw+iUaNGAIBnz57B0dERzs7OSp9wmpubi5EjR2LOnDmwt7cv/wF56vEJQhVOCVV17Orw4cNcXcbGxsX2g1SE06dPsxEjRrARI0aUew5SVqgESOQAABf1SURBVFYWi46OZtHR0QrfWl5ZZs2aJTU4HhMTo9D2srOz2fr166VubNfU1GSTJ09WypXX3NxcNnjw4BLH7jIyMuTabYkCqxxUdezq6dOnrEaNGtwVQZprpTo+ngdnbW1dbI9PRUhKSmJz585lVatWlVplYs6cOQrZh5Gx/4WVtbU1mzZtWrFHs2bN2G+//Vbm41JglYMq9q6ys7OlBnqXLl0qdElySUpKYoGBgSwwMJCXq12qIjc3l/Xo0UNqIF6WTYP58OrVKzZhwgSmoaHBtV+rVi22bNky3nuxH08yLelRtWpVudb5osCSU0FBAbcukir1riZPnsx9Jj169FDqOlze3t7MxcWFubi4VOp5WKVJTk5mNjY23PurXbs2CwkJUVr7kZGRzM3NTWpLs9q1a7MpU6awu3fv8tJGZmbmFx9funXnSyiw5HTy5EmubS8vL6W2/TnHjh3jaqpXr57SZ4jTtAbZxcbGsoYNG3Lv0dDQsNz3X5bVw4cPS+wJtWnThm3dupUlJSUptR5Z0FVCORVdcTMzM1OJFRmeP3+OcePGASi8w//QoUMwNjYWuCryOfXr18f58+e5v6M3b96gT58+ePPmjdJqaNmyJby9vXH37l0MHjyYW8ImNDQUU6dOhYmJCdzd3eHv74+CggKl1fUlFFhyCAgIwK1btwAAM2bM4BZxE0pubi6GDRvGrcM0b9489O7dW9CaSOksLS1x7do1NGvWDEDh9IMuXbrwuv+hLNq0aYPjx4/j8ePHGD16NDQ1NQEUzuM7fPgwevfuDVNTU8ydOxcPHz5Uam2fosCSQ1HvSldXF2PHjhW4GmD+/PncXnb29vbcvDCi+ho3bozg4GC0b98eQOEy0507d8bt27eVXouFhQX279+PyMhITJ8+HTo6OtxzcXFxWLduHWxsbNCmTRusWbMG/v7+vK37JTOhz0nLQ4gxrNu3b3Ntzp49WyltfklAQAB3O4a+vj579eqVYLX8+++/bNSoUWzUqFG8rIcVHx/P4uPjBd2XUFnS09NZnz59pG6rEfrKc2JiItu1axf79ttvpe5F/fRhYGDAunXrxqZOncq2b9/OfH19WUhICEtISOD9og8FVhkVDVJqaGiw6OhopbT5OSkpKczU1JT7DBSxIgBRnry8PDZq1Cju71NNTY0tX75c6LIYY4y9ffuW7dy5k33zzTdfDK9PH1WqVGHGxsbsxo0bvNRBgVUG4eHhXG9m2LBhCm+vNB//cI8ePVrocniVnJzMgoKCWFBQEIuLixO6HKVatmyZ1E3Mw4cPZ5mZmUKXxXn79i3z9vZmnp6ebMiQIczS0lJqbldJD74WGKTAKoOP1x66efOmwtv7ko+nVTRq1EiutYn4duzYMebo6MgcHR0r7L6EynLy5EnubgUAzNbWVvAe/Zfk5OSwsLAw5u3tzbZv3848PT3ZlClTmKurK/v66695+/dCgSWjmJgYbgGzzp07K7St0rx584bVrVuXO21QlVtvaB4Wvx48eMCaNGnCfQ5169ZlgYGBQpclKLpKKKP169cjLy8PAPDjjz8KWsvEiRO5HUdmzpyJ7t27C1oPUQxra2vcunWL+/t99+4devbsicWLFyM/P1/g6oRBgSWDxMRE7NmzBwDQpEkTQZeQOXDgAHx8fAAAVlZW+PXXXwWrhShe0RZsEydOBABIJBKsXLkSHTt2lHszUjGjwJLBb7/9hszMTACFE0WF2nY+OjoaP/zwAwBAU1MThw4dQtWqVQWphSiPpqYmduzYgcOHD6N27doAgJCQENja2mLLli1gjAlcoRIJfU5aHsoYw0pNTWW1a9dmQOEOKELtkVdQUMC6d+/Ovd8VK1YIUseX+Pr6Mnd3d+bu7s7LPKzY2FgWGxsrin0JleXVq1dS+0oCYD179lT42lqqggKrFGvXruXa+OmnnxTShiw2btzI1WFnZ8fy8/MFq4UIq6CggP3++++sWrVq3M+Erq4u27dvn8qsGqIoFFhfkJ2dzYyNjbmJokL9Fnv8+DG3+Fq1atXKvXSLGCQnJ7Pg4GAWHBwsqn0JlenJkyfMzs5OqrdlZ2fH2yRNVURjWF9w4MABJCQkAABcXV3RsGFDpdcgkUjg4eGB7OxsAMDatWu5m2VVjbe3N/r374/+/fvj6dOn5TrWvXv30KVLF3Tp0gXe3t48VVixNG/eHMHBwVixYgW0tbUBADdv3kSnTp3g7u6OmJgYgSvkHwXWZ0gkEqxdu5b7s1BTGbZu3crd2Ny7d29MmTJFkDpkERUVBV9fX/j6+nIrRxDFqlKlChYtWoTIyEhMmTIFWlpaYIzh8OHDaNKkCVxcXHD27FmVWR6mvCiwPsPLy4vbYcTe3p67m16ZXr9+jcWLFwMAqlevjj179qjMFmJEtTRo0ABbt25FZGQkJk2aBC0tLUgkEpw+fRr9+vVDkyZNsGLFCkRHRwtdarlQYH3GmjVruP+fNWuWIDX8+OOPSE1NBQAsXbpUkFNSIi4NGzbE9u3bERERATc3N24KTnR0NJYsWQIzMzN0794d+/fvR3p6usDVlh0FVgmCgoIQFhYGoHBF0QEDBii9hoCAABw9ehRA4cqQQoUmESczMzMcOnQIoaGh6NevH/d1xhgCAwMxZswY1KtXD/369cP27dtFM96lIXQBqmjr1q3c/0+ZMkXpE0Vzc3MxdepU7s/bt2+Hhobq/1VZWVlh5MiRAApnaJdHx44d8erVKwDgJkuSsmvVqhV8fX0RGhqKAwcO4MiRI0hMTARQuKLo2bNncfbsWQCAjY0NvvnmG9jZ2cHOzg5mZmZCll4iNcbEO002ODiY201206ZNmDlzZrmP+fr1a5iamiIvLw86OjqIjY1FnTp1yn3csvj111+xcOFCAICHhwf+/PNPpbZPKq68vDycPXsWhw8fxsWLF5GcnPzZ19arVw/t27dHq1at0KBBA+7RsGFD6OvrC3LHh+r/2layXbt2cTc5Dx8+XOlh9fLlS6xcuRJA4Tbn69atU2r7qiI5OZk7LW/atCnq168vcEUVg6amJlxcXODi4gKJRIKQkBBcvHgR//33H4KDg5GTk8O99u3bt/j333/x77//lngsHR0dVK9eHTVq1ED16tXh4eGBuXPnKvYNCDsNrHz4njial5fHTExMuGMqc6+4Iv379+fal2crbyF5e3szZ2dn5uzsTPsSilB2dja7ceMG27JlC3N3d2ctWrSQWkiwtMfkyZMVXiP1sD7i4+OD+Ph4AIVjKLa2tkpt//Tp0zhz5gwAoH379twd+mIRGRmJ06dPAwAWLVokcDWkrLS1tbnxqyJpaWmIjo5GfHw84uLiuMf79++RkZGB9PR07r/KOBuhwPrIx4PtHw96K0NmZia3EoO6ujq2b98u2KoQhBSpWbMmrK2tYW1tLXQpAGhaA+fRo0e4fPkyAKBu3boYMmSIUttfuXIlXr58CQCYNGkS2rZtq9T2CREDCqz/t23bNu7/x40bx92bpQwRERHYsGEDAMDQ0BC//PKL0tomREzolBBAamoqDh48CKDw3qxJkyYptf2pU6ciNzcXALBu3TrRzjuysbHB999/DwAwMDAo17E6derEbdJZs2bNctdGKgYKLAAHDx7kblNwcnKCqamp0to+fvw4AgICAADdunWDu7u70trmW9++fdG3b19ejqWlpQVDQ0NejlWZpaSklOsCSOvWrTFu3DgeKyofCixInw4qc7A9Pz8fCxYsAABoaGhI1VHZJScn4/79+wAAc3Nzmoclp3fv3uGPP/5AgwYN0LVrV7Rs2ZJ77q+//kJ4eDjU1NSwYsUK7utPnjzBlStXEB0djV69elFgqZKAgACEh4cDKFxf6Ntvv1Va27t27cKzZ88AAJMnT4aVlZXS2laE48ePY9++fQCAzZs3o3nz5nIfKywsjNst5vfff8e0adN4qbGySU1NhaGhIe7du1fsdqk7d+4gPDwc6urq3J0VRRhjGDlyJKKiopRZbqkq/aD7p/cNKmv5lvT0dHh6egIovFdu6dKlSmlXkZ4/fw4/Pz/4+fnRelgqIjU1FTNmzCjzvZ1qamrw9PT84q07QqjUgRUbG4tTp04BKFxvavTo0Upre926dXj79i2AwkmW5b1ZmJCSZGVlyb1vZbNmzZQ6niuLSn1KuHPnTkgkEgCAm5sbdHV1ldLu69evuWkM5ubmmD59ulLaJZVPeS+C+Pv781QJPyptDys3Nxe7d+/m/qzMwXZPT09kZGQAAFavXg0tLS2ltU2ImFXaHpa3tzfevHkDAOjatStsbGyU0u6TJ0+4XaTt7e3h6uqqlHaVwdraGqNGjQLAz3pYRfd11qpVq9y1kYqh0gaWUPcNLliwAPn5+VBTU8PGjRuV1q4yODo6wtHRkZdjaWtrw9jYmJdjkYqjUgZWWFgYgoODAQBGRkYYNGiQUtq9fv06Tpw4AQAYMWKEIBtbiEVKSgoePHgAAGjSpAlMTEwEroiogko5hnXv3j3o6OgAACZMmABNTU2ltFu0uJmOjg5WrVqllDaVydvbG05OTnBycuJlX8KuXbuia9euXMgTUikDa9SoUUhISMDWrVuVtubU6dOncfXqVQCFu/BUxB1woqKiuBUqaR5WxZaSkoJ169YhMDBQqe1WysACAF1dXUyZMkUppxoSiQTz5s0DULgaw/z58xXeJiGKEBsbi/nz56Nhw4aYO3cud6eGslTawFKmffv2cbf/LF++HDVq1BC4IkLkI5FIsGTJEsHGFCmwFCwzM5O77cbGxgZjx44VuCJC5NeoUSPo6Ogo7ULVpyrlVUJl+uOPP5CQkAAAWL9+PapUqSJwRYrTsmVLbnkcPuZhxcbGAoDS7kAgshNqjTIKLAWbPHkycnNz8fjxY/Tu3VvochSqX79+UrsMl4e2tjYtKUOKocBSsJo1a9IOMnJITk5GaGgogMKbcBs0aCBwRRVP0Z0EEokEcXFxovgFQWNYhDfe3t7o378/+vfvX+55WGFhYejZsyd69uwJHx8fniokRV6/fs0tkAiA27RW1VEPi/AmKioKvr6+AIAlS5YIXA0piZeXF/7991/cuXNHqkc1Z84cHDlyBI0aNVLpTVAosAipRIYOHYqhQ4cKXYbc6JSQECIaFFiEENGgU0LCGxsbG4wZMwYAP/sSFq1XRncGkCIUWIQ3fO9LWK9ePV6ORfjHGBOkXTolJCopOTkZgYGBCAwMRFxcnNDlkE/8888/AArXeIuMjFRau9TDIrw5duwY9u7dCwD47bffYGFhIfexaF9C1fT69WuEhYVh+fLl3NfCw8Ohp6enlJ2fKLAIb168eIHz588DKNwPj1Q8RkZGMDIyEqx9OiUkhIgGBRYhRDQosAghokFjWIQ31tbWGD16NAB+5mEVrSMm1NpLRPVQYBHe8LkvoZaWlqCDu0Q1UWARlZScnMztS2hubk77EhIANIZFeHT8+HGul8XHelhff/01vv76a9qXkHAosAhvnj9/Dj8/P/j5+dG+hEQhKLAIIaJBgUUIEQ0KLEKIaNBVQsKbli1bwsPDAwA/+xIW7epSq1atctdGKgYKLMIbvvclNDY25uVYpOKgwCIqKTU1VWoeFk0iJQCNYREenThxAk5OTnBycsKzZ8/KdazQ0FDY29vD3t4ex48f56lCInZqTKi1TnkQHBwMe3t71KlTB9nZ2ahatarQJVVqWVlZyMrKAlA47qShIX8HPi8vD2lpaQCAatWq0d9tBeHk5IQ///xT7u8X9Slh0SJxmpqa+PDhAzIzMwWuiBThcwG/zMxM+rutIIp+CclL1IFlYmKCtm3bwsjIiH6gCREBGxubcn2/qE8JCSGVCw26E0JEgwKLECIaFFiEENGgwCKEiAYFFiFENCiwSIm8vb0xffp03L9/X9A69u7di1mzZuH58+eC1kFUA01rIMWsXbsW8+bNA2MMmpqa8PLywoABA5Rex48//ohNmzYBAHR0dHDx4kV07txZ6XUQ1UGBRaQkJCSgTZs26NKlC2rXro3Dhw/DwsJC6T2t8PBw2Nvbw8HBAerq6jhy5AgcHBzg5+en1DqIaqHAIlJmz54NMzMzTJs2DUDhTcidO3fGlStX0L59e6XVMWLECLi6umLQoEEAAH9/fzg6OiIqKgqmpqZKq4OoFhrDIlLU1dUxZcoU7s9t2rSBh4cHjh07ptQ6TExMuLACgF69esHBwYF20KnkKLCIlHXr1kFdXfrHYvDgwbh7965S61i/fn2xrwlRB1EtdEpISpWeng5TU1O8ffu2XEvGlNfz58/Ru3dvREZGClYDERb1sEiptLW1oaGhgbCwMEHrMDAwQExMDBISEgStgwiHAouU6q+//sK7d+9w9epVQev4448/kJeXJ3gdRDgUWOSL8vPz8csvvwAAgoKCBKsjLS0NGzZsAAAKrEqMAot80d9//82NGV29ehVCDXlu374dHz58ACBscBJhUWCRz5JIJFzvqk2bNqhSpYogA94ZGRncVcNvv/0WT5484XUJZiIeFFjks44fP46IiAgAwOLFi9G9e3eZT8cuXbqEWbNmYcaMGTh69CgKCgrkrmPXrl149+4dAOCXX35B+/btcePGjTId4/bt21i3bp3cNRAVwQgpgUQiYdbW1gwAs7a2ZhKJhO3atYuNGTPmi9+XkpLCXF1dGQCph62tLfP19S1zHZmZmczIyIgBYL1792aMMbZ06VK2aNEimd7DmTNn2Ndff80AMCsrqzK3T1QL9bBIiXx8fPDw4UMAwKJFi6Curo7u3buXOn60du1avH79Gn5+fkhPT8fDhw/Rtm1b3L17F4MGDcLjx4/LVMeePXvw+vVrAIW9PADo0aOHTD29jIwMtGrVirfdqIkKEDoxieopKChgX331FQPAWrRowfLz87mv169fnyUkJHz2+8aPH88yMjKkvp6Xl8f11mbMmCFzHdnZ2ax+/foMAOvevTv39aysLKanp8dycnJkOk58fDz1sCoI6mGRYnx9fXHv3j0AwMKFC1GlShUAgJqaGrp27YqAgACp18fFxSEpKQlZWVlYsWIFqlWrJvW8hoYG5s2bBwBISkqSuY79+/cjLi4OwP96VwBQtWpV2NjY4Pr161Kvj4qK4jZy/Zienp7MbRLVRoFFpDDGsHz5cgCAubk5hg8fLvV8mzZt8Pfff0t97eDBg4iKikK1atVgaGhY4nENDAwAAH369JGpjtzcXKxatQoA0LlzZ/To0aPUOjZt2lSmQCTiQ4FFpJw7dw537twBACxYsKDYvYPt27fHmTNncOrUKeTl5SEmJgZeXl6oV6/eF497/vx5WFpaYujQoTLVcejQIcTExAAo7F2pqalJPd+uXTvs378fgYGBYIwhIiICFy9eRK1atWR9q0SMhD4nJaqjoKCAdezYkQFgjRo1Yrm5ucVek52dzaysrBgAVrNmTaampsbatWv3xePm5+ez5s2bsytXrshUR25uLjMzM2MAWLt27VhBQUGx1yQlJTFjY2MGgOnq6jIAzMXFpcTjZWVl0RhWBUE9LMIJDg5GeHg4dHV1sXDhQmhqahZ7jba2Ng4cOICWLVsiLS0NRkZGJS4F87H9+/fDwsICXbt2lakOHx8ffPjwAbq6uliyZEmx3hUA1K5dG3/++SfMzMyQkpKCpk2bYtmyZbK9USJatLwMkUtubi5CQ0PRokUL6OrqfvZ19+7dw5gxY+Dv7w99fX3e60hPT8ejR4/QqlUr6OjolPia7Oxs6OjowMrKCo8ePeK9BqI8FFhEYe7fv48RI0bg3LlzaNCggWB1UGBVHMKtxkYqtA8fPuC7777D7t27BQ0rUrHQGBbhXUpKCgYOHIjNmzcX25br3bt3iI2NFagyInbUwyK8SklJQf/+/dG9e3doaGjg0qVL3HPv3r3DypUraasuIjcawyK8SU5OhoODA27duvXZ1zg7O+PUqVNKrKpwxVQ3NzfUq1cPPj4+6NixY4lXHonqo8AivImIiOAmnX5O+/btYWFhoaSKCpe5ef/+PbKzs7mvWVhYKHWPRcIfCixCiGjQoDshRDQosAghokGBRQgRDQosQohoUGARQkSDAosQIhoUWIQQ0aDAIoSIBgUWIUQ0KLAIIaJBgUUIEQ0KLEKIaFBgEUJEgwKLECIaFFiEENGgwCKEiAYFFiFENCiwCCGiQYFFCBENCixCiGhQYBFCROP/AMpfyiV7Y204AAAAAElFTkSuQmCC)
physics-General
physics-
A hollow sphere of inner radius R and outer radius 2R is made of a material of thermal conductivity K. It is surrounded by another hollow sphere of inner radius 2R and outer radius 3R made of same material of thermal conductivity K. The inside of smaller sphere is maintained at 0°C and the outside of bigger sphere at 100°C. The system is in steady state. The temperature of the interface will be :
A hollow sphere of inner radius R and outer radius 2R is made of a material of thermal conductivity K. It is surrounded by another hollow sphere of inner radius 2R and outer radius 3R made of same material of thermal conductivity K. The inside of smaller sphere is maintained at 0°C and the outside of bigger sphere at 100°C. The system is in steady state. The temperature of the interface will be :
physics-General
physics-
A metallic rod of cross-sectional area 9.0 cm2 and length 0.54 m, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of 1 gm for every 33 sec. The thermal conductivity of the rod is
A metallic rod of cross-sectional area 9.0 cm2 and length 0.54 m, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of 1 gm for every 33 sec. The thermal conductivity of the rod is
physics-General
physics-
Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperature of 200°C and 20°C respectively. The temperature of junction B will be:
![](data:image/png;base64,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)
Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperature of 200°C and 20°C respectively. The temperature of junction B will be:
![](data:image/png;base64,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)
physics-General
physics-
Twelve conducting rods form the riders of a uniform cube of side 'l'. If in steady state, B and H ends of the rod are at 100°C and 0°C. Find the temperature of the junction 'A'.
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)
Twelve conducting rods form the riders of a uniform cube of side 'l'. If in steady state, B and H ends of the rod are at 100°C and 0°C. Find the temperature of the junction 'A'.
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wZJjdV/l5oNBquXr3Kpk2biI+PJz8/n4iICF588UV9h3/jDOG7IULjLzSuHtWjRw9cXV1p164d33zzDTExMZw8eZKZM2fi5uYm+jpaATMzM7y9vZkwYQJ+fn6sWbOGrVu3cvHiRWbPnq0/pzd1DQ0NnDlzBrlcjp2dHfb29lhYWKDVasnJyeE///kPP/zwAxkZGYSHh/PMM8/QpUsX1Gr1nfVZ/AURGneo8erK9OnTCQwMZOvWraxfv57Lly8zceJEwsPDsbOza5b3qq2tJTU1lbNnz5Keno6VlVWTI2FdXR35+fl07NiRgQMHmtywaFPW2Nk9dOhQPD092bZtm36uymOPPcbQoUNvuWSgKaioqOD06dPs3buXw4cP668U2djYYGVlhVQqJTc3l4yMDIKCgpg9ezZ9+/bFx8dHf7+g5iA+bQaQyWS4ubkxatQo2rdvz5o1a4iPj+fy5ctER0czfPhwfH19m2XqtYODA5mZmXz22WeEh4cze/Zs/XO1tbUUFRWRmppK3759RWjcBYVCQXh4OG3atMHT05NvvvmGtWvXcuHCBSZMmEDnzp1N5vdaXl5Oeno6CQkJ7NmzhyNHjlBVVdVkuHljgAQFBTF27Fj+8Y9/6Fc4a+6rRKbxW2lllEolHTt2ZMmSJfj5+REXF8dnn31Geno6EyZMICgo6J5mEZqZmeHl5UVISAgymQwXFxeGDh3a5DVBQUFkZ2eb1GXD1sjV1ZUZM2YQFBTE5s2b2bdvH2lpacyZM4cuXbrg7Oxs7BKprq7mxIkTHDt2DJ1OR0BAAMnJyTctE9E4k/vvf//7fQ08cfXkLkkkEmxtbZk7dy4rVqygU6dO/Pvf/2b+/Pns37+fgoKCe17k589mI7Zr147+/fuLjthmYGZmxqBBg1iyZAljx44lLS2NF154gc2bN5OZmWn0ld6cnZ0ZP348K1euJCYmhrFjx97UkWlra8ugQYMYPHjwfW8hidC4RxKJhO7du/PJJ5/wwgsvkJGRwezZs3nrrbe4evXqffnA1dXVkZubC5jeKlStlUQiwdvbm5deeonPPvsMW1tbli5dyowZM8jIyKCmpsYoK73pdDpqamq4evUqhw4dYs6cObz11lv6dTEah6CHh4czevToFpkrJT5xzcTBwYG5c+eydetWOnfuzBdffMGgQYO4cOFCswaHTqfj6NGjXLp0qdWtg9kaWFhYMGDAAHbu3MnUqVNJSEigX79+7Nq1i4qKihavp7Kykq+++orBgwczbtw4cnNzWbhwIa+//jr29vbodDrs7OwYNmwY3bp1a5GaRGg0I5lMRnh4OB9//DErVqwgKyuLgQMH8tprr5GXl3dXR6ra2lrOnDnDkiVLWLJkCfPnz2fatGmcPHnyPuyBAL+33tzc3Fi4cCE7d+5EqVTy/PPPM3fuXE6fPt0iNZSXl7Ny5Ur69+/Pyy+/jEajYcmSJRw+fJiJEyeybt06rl+/jlqtZt68eTzxxBMt1uoUHaHNTKlU4uHhwbhx4wgMDOTtt99m48aNHD9+nFdeeYXIyEiDmpAKhYKAgACmTp0K/D5wJyoqymR69h9UMpkMW1tb+vfvz3fffceqVatISkriwoULPP/88zzyyCPNPvFNp9NRUVHBRx99RHx8PJcuXcLLy4uXX36ZESNGoFarUSgUxMXFYW1tzZIlS+jXrx++vr4temsO8cm7D2QyGfb29vTp0wc3Nzd27NjBli1bePnll5kwYQIjRoy447EAUqkUc3Nz3Nzc9I/Z2dlRVlYmOkHvs8ZJZGFhYcTExLB7926++uor3njjDVJTU3nyySebZZFijUZDXl4eW7duJTExkTNnzuDn58f06dP140YcHBz0y/p5eXnx4Ycf4u3tjZ2dXYsfQERo3CcSiQSVSkVoaCiurq60bduW1atXs2bNGo4fP86kSZPo06fPXf3BLS0tsbCwoKqqisrKShwdHcWI1PuocR7S+PHjm4wkTU5OZuLEiYwcOfKutqvRaEhLSyMhIYGEhASOHTuGh4cHkyZNYsiQIQQHB+vDopFCoaBbt27NOljLUCI0WoCrqyuPPfYY7u7ubN++nV9//ZWsrCymTp3K4MGDm7Qi7pROpyM1NZVr164xcODA+1C18EcSiQQnJyeGDBmCu7s7W7du5cCBA7zxxhvk5eXxj3/8A2dn5zs6CGg0GlJSUvjtt9/Yv38/x48fx87Ojscee4zBgwcTERGBra3tLQ8Eja0fYxKh0UIa78sRGBhIXFwcX331FUuWLOHSpUuMGDGCTp066fs66uvrKS0tJS8vj+rqavLz8zly5EiTjq7S0lIOHjxIjx49RCujBZmZmdG1a1fUajUhISFs3LiRmJgYsrOziY6OJiQk5LYD+zQaDampqaSkpPDdd99x8uRJLC0tGTRoECNHjqR37973NCiwpYjQaGFqtZpp06YREhLC8uXL2bhxI/v27eONN94gIiICGxsbampqSE1NJTc3l5CQEHQ6HZs3b24yJLigoIDOnTub7N3PH2SNyweOHz+esLAwFi5cyKZNmzh69CizZs2iT58+ODg46EO+traWnJwcLl++zMqVK0lOTsbc3JzevXszbtw4unfv3irCopEIDSMwNzenf//+hISEsHbtWlavXs24ceN44403GD58OI6OjnTt2pXw8PA/3U7jfTwE4zAzM6NLly7s2LGDlStXEhsby7x583j22WcZO3Ys1tbWVFdXk56ezqJFizh79iwqlYqoqCief/55OnfurL8ZUmsiQsNIGo9WCxYsYPTo0TzyyCPMmzePf//737z++ut069btjjq6HtQBXn+8B6up76O5uTkLFy5k4MCBzJ07l9dee42DBw/qB4kdPXoUiUTCiBEjWLRoEYGBgSa5TumdEqFhZHK5nMDAQH788UeWL1/ON998w7/+9S+GDh2Ko6OjscszmtTUVAoKCkhOTuaLL74wdjl3pKGhgcGDByOVSjl06BCJiYlYW1vz5JNPMm/ePP0U9dbeByVCwwQ0zmRduHAh165dIyEhgQ8++OChnsFaW1ur7wROTU01djl3rPEWivX19VhZWTF8+HCWLVuGo6PjAzMg78HYiwdA4x2y7O3tqaqqYsSIETdNh3+YnD17lh07duDj48OkSZOMXY7BDh06RHx8PM7Ozri6uhq7nGYlQsMEabVaQkNDGTNmjLFLMRpbW1sOHjyIn59fq/w9VFVVsX//fv0NnIuLi8nNzUWr1epfY2dnh5ubG0qlkqKiIgoKCppsozFwTK2zVISGCZJIJMjl8lbdWXavFAoFUqm01f4e/nfFLK1WS15eHhs3bqSuro4BAwbo+z8kEgn19fWcP3+eL7/8EnNzc8aMGWOyN7AWs1wF4T6TyWS4urrSu3dv0tPTOXnyJGq1moCAACwsLFAqlajVaiIjIzl27Bjnzp2jQ4cOeHt7/+WtGI1BtDQEoQVIpVLs7e1xdXVFo9FgZ2fXZMKhQqHA0dERJycn7O3tsbKyMtmOU9HSEIQW9mfLODY+b8pMM8oE4QHWOGjtj52iwE3/NlUiNAShhdXX13P58mXOnz/f5PGysjLq6uqMVNWdE6EhCEZQWVl505qjFRUVraK1IUJDEFqYXC6nbdu2dOzYscnjpaWlreLysggNQWhhUqkUMzOzmwZt1dTUmHwnKIirJ4IgGEiEhiC0EK1WS2Vl5W2n+ms0GiorK41yUyZDiNMTQbjPtFot5eXlZGdnU11djUqlIjc3l7y8POzt7ZHL5dy4cYNz584hlUpRKpVkZmZiZ2eHnZ2dyS20JEJDEO6zhoYGsrKySEpKIjo6Gvh9ucbffvuNnj17YmFhQXJyMseOHWPq1KlIpVLOnj2LTCYjIiJChIYgPGyUSiVhYWGEhYXd9jVRUVFERUW1YFV3T/RpCIJgEBEagiAYRISGIAgGEaEhCIJBRGgIgmAQERqCIBhEhIYgCAYRoSEIgkFEaAiCYBARGoIgGESEhiAIBhGhIQiCQURoCIJgEBEagiAYRISGIAgGEaEhCIJBRGgIgmAQERqCIBhEhIYgCAYRoSEIgkGahEZlZSUrVqzg2rVrt7z3QlVVFQcOHGDy5Mls376dsrKyW260uLiYhQsXEhMTw8WLF6mvr2/yfGlpKdu3b2fs2LF8/PHHN93TslFZWRk7d+5k7NixPPHEE8TFxVFaWsqlS5dISUmhoaHhbvdbEIS7JAXIyclh6dKlDB06lPfff5/y8vKbQiMtLY23336bxMREZs2aRXl5OcuXLycjI0P/msrKSvbt28dzzz1H7969GT16NMuXL+fAgQNUVlYCUFRUxN69e8nKymL27NkEBATwzjvvkJeXp9/O9evXiY2NZdKkSaSmpjJr1izmzZtHcHAwn3zyCdOnT2fnzp2t4g7bgvCgkQJYW1vTuXNnbGxsyM/Pv+kIfuPGDQ4ePEhCQgKjRo2iW7duDBkyhLS0NHbv3k1BQQEAly5dYvPmzQQFBdG3b186depEREQEn332GadOnUKr1ZKdnU1KSgpjxoyhe/fu9O7dG7lcTmZmJtXV1VRVVREfH8+mTZsICQnh0UcfpXfv3nTv3p2AgACGDRuGq6srZWVl1NbWtvxvTBAeclIAe3t7evToQZ8+fW55A9orV65w4MAB7O3tCQ0NRSKR0KZNGwICAti1axepqak0NDSQnJxMWloa/fv3x8LCAolEwpAhQ7h8+TKJiYmUlJRQUlKCRqPBy8sLiUSCpaUlTk5O3Lhxg4aGBk6fPs3GjRuRSqVMnToVf39/fU1SqZTOnTszffp02rZtK1oagmAE+pslSaVS/Rf9f125coXc3FyCg4ORyWT6x4ODg4mLiyMzM5MOHTqQkZFBdXU1jo6O+td4eXnh5OREcnIyRUVFeHh4IJPJOHToEF26dCE7O5vCwkJ9i+PgwYOkpaUxatQofHx8bll0aGgoLi4umJmZ3dFOlpWVkZqaSk5Ojv60SyqVIpfLsbGxoU2bNnh6et52/wVB+P/u6A5rxcXFlJaWYmFh0eRxT09PpFIpV69e5cqVK2RkZCCTyZp8mWUyGe7u7hQWFlJSUkLnzp0ZPHgwu3fvRqlUcvr0acLCwvDy8qK+vp6LFy+iUCgIDg6+7RfY0dGxSTD9lYqKCo4ePcrGjRs5ffo04eHheHt7Y21tjbW1NTY2Nnh5eREeHk6nTp2QSsVFJUG4nTsKjaqqKhoaGnBzc2vyuFKpRCaTcePGDa5fv05JSQkKhQJra+umbyKXU1FRQVlZGebm5vTq1Yvu3btz7do1IiIiUCgUSCQSLl26RHFxMdbW1rRp06bZdtLDw4PJkyfj4ODAxIkT+ec//8mwYcOwsLCgoqKCrVu3snz5cpydnfnuu+9wd3dvtvcWhAfNHR1SJRKJ/r8/0mg06HQ6/f9v1zLQarU0NDSg0Wj0j8nlclxdXVEqlfqfMzMzQ6lU6rfZnBQKBT4+PjfVaGVlxZNPPsmsWbPIyMggNja2Wd9XEB40dxQacrkcmUx201WVoqIiampqsLOzw8rKCjMzM3Q6HVqttsnriouLsbCwwNbW9k/fx8PDA2dnZ27cuEFOTo6Bu3LvamtrycrKavH3FYTW5I5Cw9XVFRsbGzIzM5s8np2djZOTE8HBwfj5+REYGEhtbS3Xrl3Tv6a8vJzCwkJCQkLw9fX90/eRyWT4+PhQU1PD8ePHbwqfP7pVON0pnU6n7xDVaDQcPXqUb7/9Fjc3N6ZOnXpX2xSMT6vV6lu9jf74txaaxx31afj7+xMSEsL58+fRarX6jsLz58/j7e2Nj48P9vb2dOzYkcTERPLz8+nYsSMAycnJVFdX06FDhzvqvOzTpw+JiYkkJydz+PBhevbsedMpRW5uLnl5eQQEBGBvb2/oPrN06VLWr1+PVCqlpqaGwsJCXF1diYmJITg42ODtCcaj1WrJysoiLi6O/fv3Y2VlhVKp5Omnn0atVpOWlkaHDh3w9vY2dqkPDH1oaLVaqqurAW5Kaw8PD0aMGEmH/oYAABPFSURBVEF+fj4//fQTPXr04NixY2RnZzN58mR8fX2Ry+VEREQwcOBA4uLi6NmzJ0qlkm3bttGzZ0969ux5R5dIQ0JCmDVrFhs3biQmJobo6GjGjx+PpaUlABcuXCAzM5OAgICbrubcqSFDhhAREYFSqaS0tJTExER+/vlnduzYgYeHB2FhYXe1XaFlVVdXs23bNhISEggJCWHmzJnY2Nig0+lQKBT8n//zf1CpVLRp00aERjOSw++nECkpKVy/fp1evXrxyy+/IJPJUKvVmJmZYW5uTvfu3ZHJZJw6dYozZ84gk8mYMGEC/fr1w8bGBgB3d3fGjRvHt99+y7Zt29BqtajVaoYNG3bLTshbsbGxoW/fvri6upKQkEBKSgqffPIJcrkctVqNnZ0dISEhuLm53fE4jf/VtWtXhg4dioWFBVqtlm7durF69Wq2b99OSUkJa9aswd7eXozZMGEajYbvvvuOTz/9lNDQUJ544gn8/Pz0z1dXV9OvXz+SkpL0UxiE5qFvaVhZWTF06FCGDh36+xPypmcuTk5O9OvXj7Zt23Lq1ClCQ0Px8fFp8sVVKBT4+fkxc+ZMjh8/TlVVFX/729+wsbEx6AtoZ2dHZGQkYWFh+pZFVVUVfn5+BAcHY2dnd6/7rSeVSgkMDOTxxx9n7969/PTTTxQVFWFra9tkIJtgWkpLS4mNjcXc3JwJEyY0CQwAc3Nzxo8fT3Z29l33fQm3Joff557cSZPczMyMgIAAAgICbvsaiUSCra0t/fv3v+fiLCws6Ny5M507d77nbQG37RDT6XTI5XIsLS0pLy+/6xaM0HJ++eUXrly5wpAhQwgPD7/laywtLYmKisLFxaWFq3uw3VFHaGun0+mor6/XT/m/ceMGN27c0D9eXFzMwYMHuX79Or1798bT01O0Mkzc119/TW5uLh4eHvrT41sZMmRIC1b1cGjR0NDpdNTV1VFTU9PkqC+XyzE3N79vX1SNRkNhYSG//vorLi4uHDt2DJVKhZeXF0VFRezcuZMjR44QGRnJxx9/jEKhuC91CM1Dp9Nx5coVamtrRavQCFo0NGpqakhMTGTnzp3U1NToH/fz82Py5Mmo1er7Ehw6nQ5bW1tefPFFXnzxxSbPhYaGEh0dfVMfjmC6JBIJjo6O+sGEQstq0W+KSqWiX79+aDQaXnrpJXJzc4HfB3WtXbuWmJgYHnvsMRwcHJr1fRUKxW23eavh8YLp69KlC0eOHOH69etoNBpxOtmC7ik0NBoNlZWVBi27p9Pp6NSpE++99x4ffvghCQkJ6HQ6qqqqeP3119m/fz9PP/00kZGRd/VlrqmpuWVvuZi5+mAZMWIEO3fu5NSpU6SmptKhQ4dbvq6yshKpVIq5uXkLV/jguqfQyM3NZfHixaSlpRn8s7W1tU3ml+h0OgoKCti7dy/Jycm4ubndVWiUl5dTUlLC9u3bOX/+PEql0uBtGNOhQ4eorq5m586dD/U8mNzcXK5cuYK9vT2JiYlERUU1aU34+/sTERHBDz/8wH//+198fX31AwAblZaWcvz4cQICAvDy8mrpXXhg3VNoKJVK7Ozs7up0or6+nrq6OoqKipqcl2o0GqysrPDz87urDsm8vDyuXLnCiRMnOHnyJEqlUj+FvzVoXMHsxIkTXLx40djlGI1Go0EqlZKSkkJMTAxPPPEEU6dO1QeDubk5U6dORaFQ8NNPP1FcXEx4eDg9e/ZEo9GQlZVFXl4e/v7+zTquR7jH0HBycuK5556jvLz8jn9Gp9NRVFTETz/91ORIKpPJCAoKon///owcOZJ27drdVefk5cuXSU5O5r///S+//fYbpaWldO3alf79+//ppTlTERcXx88//8zQoUPp06ePscsxKqlUSnFxMUlJSaxcuZJr167x1FNP0bZtWxQKBWFhYcyePZtjx47x66+/cvbsWaqrq1GpVKhUKnx9fQkKCmoVf/fW5J5Co3EE6J3SarXk5uaSkJDAf/7zH7KysvR/4C5duvDMM8/Qp0+fmxb7MUSbNm3o0aMHkZGR7Nixg2+//ZbCwkJsbGwYPnw4Xl5eJt2/cfHiRY4dO0aPHj147rnnjF2O0VVVVdGvXz9WrlzJ559/TlpaGuPHjycyMhI7Ozt8fHzw8fFhxIgRFBcXU1JSgo2NjRhrcx+16NUTjUZDRkYGWVlZhIeH60fyOTo6Mm3aNPz8/JrtDx0cHIy3tzchISG89957vPvuu5w/f55JkyYREhKCSqUSV01aAQsLC3r16oWXlxfLli3jhx9+4NixY7z44otER0fj6uqKXC5HpVLh6emJp6ensUt+4LVoaCgUCvr27Uvfvn1b5P0sLS0ZNWoUgYGBvPnmm3z77bckJCSwYsUKIiMjsbGxEUejVkAikeDl5cWqVav473//y9tvv83ChQvJzMxkypQp+Pj43PWMZ8FwpttOb0bBwcGsXr2axYsXU1xcTHR0NOvXr6eoqKjZlxUU7h8zMzPGjBnDvn376Nu3L6tXr2batGn88MMPVFdXi4FeLeShCA34fcr9xIkTOX78OF27duXNN99k2rRpHD16VARHK2Nra0tsbCwxMTEUFBQwbdo0Fi5caFCHvHD3HprQkEgkmJmZ0aZNG7755humTZvGhQsXePrpp/nwww+5ceOGsUsU7pBEIsHKyorp06ezfv16oqKi2LJlC08++SQnTpwwdnkPvIcmNBpJpVLUajVz5sxh8eLFuLq68tFHH7Fw4UJSU1NFE7cVsbOzo1u3bixZsoRZs2aRnJzMrFmzWLZsGaWlpeJveZ88tLO0PD09GT58OD4+Pqxbt479+/dz+fJlnnrqKcaMGaO/F4tg2szNzQkICGDGjBm0adOGbdu28dlnn5Gens7cuXMJCAhodaOCTd1DGxrwez9Hjx49cHR0xNPTk927d7N06VIyMzOZMGEC7u7uYvZrKyCVSvHw8OCpp57C39+fbdu2sWvXLq5fv87kyZOJjIzEyclJHASayUP/jZBIJLRr145nn32W4OBg1q5dy7vvvkteXh6TJk0iKCgIKysr8YFrBaytrenbty8dO3bEw8ODrVu38vbbbxMdHU10dDT+/v7iINAMxG/w/3FxcWHUqFGEhYXx1ltv8d1335Gdnc348ePp06cPLi4uYkxHKyCVSnF2diYmJgYvLy9iY2P54osvSElJ4YUXXqB9+/Y3TWwTDPPQdYT+GYVCQWBgIJs2bWLmzJlkZGSwcOFC1qxZQ3Z2NnV1dcYuUbhDMpmMp59+mlWrVjFo0CASExOZO3cu+/fvp7i4WHSS3gMRGrcglUp57bXX+Pjjj/H19eXdd9/lX//6F2fPnqW2ttbY5QkGCA0N5b333uOVV17h8uXLPPvss7z99ttcvXpVjM+5SyI0/kRUVBTffvstM2bM4Mcff2T8+PFs3rxZtDhaGXNzc6ZPn87XX39Nhw4d+OSTT+jXrx+XLl0yaAEp4XciNP6EVCrF1taWmJgYVq1ahY2NDa+99hpjx44lPz9fNHFbEblcTqdOnVi9ejVLly4lPz+fQYMGsWHDhib3Hhb+mgiNvyCRSLCzs2P48OG89957PPLII/z44488+uij7Nu3j8rKShEerYSZmRleXl5MnDiRLVu2YG9vz9tvv82cOXP47bffqK+vN3aJrYIIjTtka2tL165deemll1i0aBH5+fksXLiQlStXkp2dLc6PWwmZTIaDgwMDBgzg008/ZeDAgRw9epT58+ezfft2SktLjV2iyROXXA1gZmaGn58fU6ZMwcXFhQ0bNhAbG0taWhrTpk2jS5cu4nJeKyCRSFAqlfTq1QsXFxfat2/PV199xXvvvUdWVhbR0dG0b9/epBdrMiYRGgaSSCTY2Njw+OOP4+PjQ2xsLPHx8RQUFDB9+nR69eqFu7u7GAzWSgQEBPDMM8/g4+PD6tWr+eqrrzh37hyTJ0/mb3/7m1jF/BZElN4lmUxGZGQkixcv5oUXXqCwsJB33nmHtWvXkpKSIs6PWxErKyv+8Y9/8OabbxIVFcXp06dZsGABO3bsoLCwUJx6/g8RGvfI0dGRuXPn8uabb+Lg4MCGDRtYtGgRx44do7Ky0tjlCXdIKpUSERHB66+/zssvv4xOp+Oll17i888/59KlS2KRnz8QodFMoqOj+eijjxg9ejS//vor48ePJz4+ntLS0lvevEkwTc7OzkyYMIGNGzcSHBzMu+++y8yZM/nll1+oqKgQf0tEaDSrdu3asWzZMtauXQvAhAkTePXVVykqKhIftlZELpcTFhbGf/7zH+bMmcOpU6cYM2YMmzZtEos1IUKj2SkUCgYNGsTOnTsZNGgQX375JQMGDCApKYmqqipjlycYwMLCggULFrB7926CgoL0/VcnT558qE9VRGg0s8ZlBQMDA1m1ahXLli2jsrKSmTNn8tFHH5Gbm/tQf+Bak8ZlBcPDw9mwYQOjRo3iyJEjzJo1i7Vr11JRUWHsEo1ChMZ9olAo8PHx4cknn+Tzzz/H29ubzZs3s2jRIg4ePCjmr7QiKpWKwMBA5s+fz4svvohcLmfFihXExMSQnp5u7PJanBincR9JpVIcHBwYNGgQNjY2bN68mZ9//pmsrCzGjRvH6NGjcXJyMnaZwh2QSqX4+fnxxBNP4O/vz5dffsmuXbvIz89n3LhxDBgwAHNz84difI4IjRYglUqJjIzE0dGRdu3asX37dj744APy8/N57LHHCAoKEqMPWwknJyf69euHWq1m3bp1fP/99yxevJjMzEweeeQRPDw8HvjVwR7svTMx7dq1w8PDg44dO7Jq1Sq+/PJLzp8/z4wZM8QQ9FZEqVTSvn17FixYQFBQEBs2bOCdd97Rry3brl272/5sVVUVVVVVNw0Yk0gkyOVyzM3NTf6WoSI0WpiVlRUDBw7E09OTjz/+mPj4eE6cOMGrr77KgAEDqK+vFx2lrYBEIsHZ2ZnJkycTERHBkiVL+Prrr8nKymLKlCkUFxff8ufy8vI4deqUfi0Pe3t7bGxs0Ol0+ikK3t7eeHp6YmdnZ5KtFtOr6CERFBTEW2+9pf/AzZgxg7lz5+rX6dBqtWKBmFZAIpHQoUMH1q5dy9KlS/n6669JSUnB1tb2ln8/f39/SktLWbVqFWVlZUybNo2QkBCqqqo4ffo0X375JZcvX2bSpEk8+eSTeHp6mlxwmFY1Dxk7OzsmTJjA0KFDGT9+PB988AE1NTVIJBKKioq4cOGCsUsUDDBx4kQcHR1Zv349J06cwMHB4Zav8/b2xsnJCWtrayIjIwkPDwegd+/eTJs2jblz57JixQqKi4uZM2cOarW6JXfjL4nQMLLG1bN37NjBu+++y/r16ykoKOCjjz5i9erVxi5PMFB9fT11dXVIpdK76qNSKpUsWbKE9PR0vv76awIDA3n66adNaiV8ERomoHEQ0ezZs+nQoQMXLlxAq9WKvo1WTCqVYmVlRWhoqME/a2try4QJE1i8eDEJCQn06tWL4ODg+1Dl3RGhYUIcHR0ZPHgwUVFRIjBaOYlEglQqxczM7K5+NiAgACsrK9LS0sjNzRWhIfxOo9FQXl6u7zWXSCTY2toauyzBBFhYWKBSqSgvLze5DnExosiIrl+/zrp169i8eTM1NTXGLkcwITU1NdTV1eHs7Iy9vb2xy2lCtDSMRKfTUVBQwOeff45Go2HMmDGYmZmJkaECAOfPn6esrIxu3bqZ3NUT8Qk1ksrKSjIzM7G0tOTy5cucPHlS3L1NAODq1avs2rULuVxOjx49cHd3N3ZJTYjQMJKcnBwOHTrEW2+9hZWVFWvXruXatWuiA/QhoNFo9AP4NBoNDQ0N1NfXU1VVRX5+Plu3buX8+fMMGTKEyMhIk7rcCuL0xCi0Wi2ZmZlkZ2fTpUsXevbsyZ49e3jxxRdxc3MzuRGAQvNpaGigtLSUqqoqamtrycrKwsnJidraWrKzs9myZQuHDx9m8uTJTJkyBU9PT2OXfBOJThzaWlxhYSEJCQlYW1szdOhQcnJy6N69Oy+88AIzZ87ExcXF2CUK98nevXvZt2+f/gZbcrkcqVSKXC5HrVYTFRVFREQE1tbWKBQKk5y4JkLDCOLj49m3bx8xMTHY29tTW1tL3759ycvLIzY2lt69e5vkh0W4d9XV1VRXV+tPURo1znJVqVRilqvQVG1tLWlpaaSkpPDpp58ilUrR6XRYW1tTUlLCyZMn6dSpE9bW1sYuVbgPzM3NW/0NmERLo4UdPXqU+Ph4goOD8fDw0D9eW1vLvHnzcHR0ZOnSpURERJj00UZ4eImWRgs7deoUSqWSoUOH3jShacCAAXz77becOXOGzp07o1AojFSlINyeuOTagnJzc0lPT8fT0xMLC4ubnh8xYgRWVlYkJiaSlZVlhAoF4a+J0GghxcXFJCUlce3aNezs7G66ZWNNTQ3Ozs64urpy4cIFfvzxR65evSrGbQgmR5yetJC0tDRKSkrw9fWlrKyMq1evYmVlpX++rKyMU6dOMXDgQOrq6igvLyctLQ1HR0fRtyGYFNERKgiCQcTpiSAIBhGhIQiCQURoCIJgEBEagiAYRISGIAgGEaEhCIJBRGgIgmAQERqCIBhEhIYgCAYRoSEIgkFEaAiCYBARGoIgGESEhiAIBhGhIQiCQURoCIJgEBEagiAYRISGIAgGEaEhCIJBRGgIgmAQERqCIBhEhIYgCAYRoSEIgkFEaAiCYBARGoIgGESEhiAIBhGhIQiCQURoCIJgEBEagiAY5P8CE+9QXBEWREYAAAAASUVORK5CYII=)
physics-General
physics-
Three rods made of the same material and having same cross-sectional area but different lengths 10cm, 20 cm and 30 cm are joined as shown. The temperature of the joint is:
![](data:image/png;base64,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)
Three rods made of the same material and having same cross-sectional area but different lengths 10cm, 20 cm and 30 cm are joined as shown. The temperature of the joint is:
![](data:image/png;base64,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)
physics-General