Physics-
General
Easy
Question
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation
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)
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid a cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
![](data:image/png;base64,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)
Imagine the depth of the block submerged in the liquid does not change on increasing temperature then
The correct answer is: ![gamma subscript L end subscript equals 2 alpha](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAARCAYAAACIJW/gAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAY1JREFUeNpjYBhcwBqI1wDxJyD+BcQXgDiaYRiBg0AcCcQ8UL4WEB+Fig1bIA/Elyg1RA2aHLABUagFWgPoyR84xIWBeCFUfiFSzDNA+aHIimcCcSyaASxAfBiIHUl00H8iMLHAEppM0QEbVNwLyt4PxFOQYv0cugYNLElhGhAXDWDMcQDxSWjhgw5qgbgSiW8AxHeh7KVAbIvNwKNIhgUB8YYB9Jwg1H43HPKP0ZIkrJByg0YMVpABxBOg+e4CNI2TAyhNokpQz6ngkDeGZh10kAzEx7F4HA7EodEMyqAeONTUA3E5DWMOlFVmAzEXHjWgwmM5FvGFOPIrCgDlw7l45FcBcQCNPCcONZ+FgDpQ9lmHJgYKlERozKrg0wxKv3x45G8BsSSNPLgFGoOEAMh996HVGyivzofWAiCwDVoA4QQ78MgxAfEXGiZPUvKsPLRqOIdW38XjaxiA6pPneBxgDsR7h3KzyAtL2kYGkdDkMGRBLFJrABuYBM3Iwxasw1N9DAvwDkvmZxvMDgYAAAdgFP+leYwAAACKdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPiYjeDNCMzs8L21pPjxtaT5MPC9taT48L21zdWI+PG1vPj08L21vPjxtbj4yPC9tbj48bWk+JiN4M0IxOzwvbWk+PC9tYXRoPmEU01oAAAAASUVORK5CYII=)
Related Questions to study
physics-
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation
![](data:image/png;base64,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)
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid A cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
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)
Imagine fraction submerged does not change on increasing temperature the relation between
L and
is
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation
![](data:image/png;base64,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)
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid A cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
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)
Imagine fraction submerged does not change on increasing temperature the relation between
L and
is
physics-General
physics-
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation
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b9ZR5+Hb+fFSc7smH/j7nECqCuN5alv9hz5lNHeoyYzpZggTraD+/k/vnL1ySMQ96hpISe5mjINc4dv8TtmIscP3ObWM9ZjJu5jM2/J9Lms7HICVfw8gsn/soJTkVkUL5Ze5qcm8+opQE8AKAK/SYOpkHbXrxrkeOWM2xE5y4yvw7vh9OSaxjViOGPbae5U64Z7ZucY/6opQQ8yFu3F/DcG0B0UiBe2/2IfHQwuqoK2dWb/lzLSSWe4p6m1m804tyin8S+xMefZJ2bIdq0+1acjQ0TV4JuiPvanD/3EV+9N0OcedHrKDmQEm+JW4kl76Sjeztnijmnn3mhp1BofL4S780488KXqUoSpXXkUARI3PTzJKLdcAbkOKuk4Ch1RYPK1BLLor9sAUiEesxl0zVBfIwVk5aUwBACeoYi2GdGTe1OH1M7z6fZUeoaFRyl7hVDpU0mOrYWw2aOpbFSJ8+NItgXjKHdh0y10/WNTFJECBFREYREpdC+ga7QT6UNNQ0GLmD9wCK4lJxEREgEUREhRKW0p7RWr3Kmk4KCHlGKZokVFEo/ypD4lUPf3OoekhrN1bA48nvXqahUxw7rZwmBp4e8GqVU+JeS7lYHOlzrAI2/K86zd3H6jD87XXrh6LwOv7O+HF4xkek7457zinpEca8rKbwIMkRK4XzqRIl2q8vOJL9rnRBCc95bZHvXaYT35Eaixid7sq+TFSK8fWOf54p6hTIkfkEkB3mweusJLoZnULuHE1OHt6eIPOpAvseuL79F+tyN0Tp96ih5bnVQeNc6oExbB3R719nyCnnXKT3si0AbtkZ8MmKNiNIKkXjJTbxXp7ro5R5WpDakB3wj7G3fE8v+epD/SyleHP68r3Dac0toM66KpW9XFY2n+AiNNlz8OmWa2B2pEcmBc8WbFm+In7zPi82jbEXFtsPEvOWbxLpJ9sKil7u4JSWK3aOHCPcYSWhvbRfTfjghpNhzwn1QA2E1+pBIF0Ikrn9HWAz2EOlCiKxri8Vb5m+LFbckIYQk7myaJFyOp+S0WHiNayz6rbsrtNFrRB/Ld8S6u5IQievFOxaDhUeB3XSeHvYVQ+lhnxuJyD2/EWKxAAs1GLb8lF+m7KL1joPw6WcFptJq0tBoC7uiZoBBShSXr8aSUWASR8Z08uCzrl0IWvIrPw+149FS5CO3uu8XWKIuI9HVsSGr7j92qxt+ageeIrdb3ZSUPnw2/iPKXLqO29DcbnUVZn3G1PEmqCob06t9beYF5bcm263Oja/dLzJmVtVst7pBOSNtPXStM8/jWlcMu8P0CUWwz43gfuIDVIb/OtRh0aIpNfY/QYxyIoH7t+JXeJ86jGtZUjE5kZSCfepI0Bgg0uO5eTOONBlMHg7JS55bHSiudc+GItgXgEAmLSXl4eyoTFJkAo369EAb6sEc111ciLdi5MIFDLB++PKmqkzbD515oU51oSvp91NVJu//ne/ftsi1xFLi3Org2V3reORdl3MaWUuoxxxcd10g3mokCxcMwLqUboNUlnVeCDKxx934Zcdxjm5fxIJ/euM6vgFh8bUZv2ob6wZEs3zNeV7egY3x7F9xko4b9vNjHrFCCXSrg2dyrQOZ2Aue7A2IJinQi+1+kWQAaMOIrz2eVdvWMSB6OWvOl96jMZWtic+NlvMzO+CsdufA8PLcU1vRpG7lXKLJOOrC1LuTWDLU/OU8IeUkbseAhaVpiXsCx+/6hpXmM5j5RlF46mRw1GUqdyctYah5SauJF4MyJH5uZNJT0ylfqwrVbOrnnzORbnAwuClOE16SWAFUpliWHJ86isutTrpxkOCmTkwopWIFRbAvABVVOo3EqZGOQ8jkRC54+mH+yRDs1BIS6pe7fa8EUdRudXLiBTz9zPlkiB1qSQJ16axpZUj80kjCf+5gvjhhQt3qMpl1BuE2731qlt6Hf/GR5M/cwV9wwqQu1eVM6gxyY/77pXN9SBGsgoIeUbqf98lX8Vozn9k/beFcnEzyVS/WzJ/NT1vOEfeUO9SfJy1Axk1ftqzYw98FnD9emkgM2MDifWEvwLmgAPK0a+FJJeLPDaw6FPHybHvJlF7BSmGsmrCclAFj6Zy8mimzpjNheQoDxnYmefUXLH2KqX8pbNUzpwVAvkOwlxuzfzpMRKkXbF4PnhdMnnb9Yun5wieNDuag2/csKqSnki6voWKn2DZFFjpo07MhRSwUXVpMFX4aIYSQRMTCLqLFVL9n8FB5nrQ5colcJLrUHS0OvYobYF8gudv1adGKkB87iqaTvf+7LQvwGipu1LNmzZr1WL6JnF7gzA8XzOnawQrDhNOsXnmZau0bU/kF98Xyna1M+vICDXq2oZqOuWrp7nn2exzgmE8Yauum1DI2AOku53dvZdeRU4RkmGNrbYYh2cGstm38jf3+sVRqbEuNhJOsW7aJvWejQaSQEPUX+/fs42w0iDQVlq3r6yyPdPc8u7fu4sipEDLMbbE2M+D2n+tYtmlv7rTEcXbTElbsPM2N8g1pVduA0APurD6poUEbK9Iv7GbrriOcCsnA3NYaM0MQD86wacNdOjm3I3HHKtwPxWLVsT4pvr+ycq03Gts2mN44xBafDKxFAGvWHiLK1I7GIpAdazdzIq4mrRpX1Vlei/I59gdqIjm1bSO/7fcntlJjGpcPw9NtOZsP/kV6vQakeS1htXcWNs0rcH2fB4EGFbnhsQqPQIk6zephqobU60f4bdthTvj+jdaqGXVNZe5e2sdvfllYpf3Jqg1/8qB2axqYqZETL3N491H8/grk76SKNK9nTOy5PWz/y5AWjauh0tVm2rtc2vcbfllWpP25ig1/PqB26waYqXM1Rr50Brf/zNGuaagsW1O/sgqQSbx8mN1H/fgr8G/up6fiu30Vh2Kt6Fg/Bd9fV7LWW4NtO2s0vhvZmerAW1mHWXsgFLVNM2qbkCt9knF1olYPZeSiK0hlwaROK2rGHctdJ8b3nlAGibvn9+Nx4Bg+YWqsm9bC2EBD5KltbPxtP/6xlWhsa0HZpLx1V4gYt7nkm35QuM5YKX4cNklsS9CKG8t7ifYuASLjpTwr0kXAN/bC9r1lIq+DiTZisxg3com4kqoVEYu7iGrdlomIzBjhMba/cDmZIKSUQPFz90ai+5IgkRH+q5gybbeI1CSLwLlvCos3FogrWUJk/TVTtGnp8vAM4Czx18w2oqVLwWfWSjEeYmx/F3EyQRIpgT+L7o26iyVBWQWmle5sFR9ZdhA/BGuFEJK4s222WHg+TcR4jBX9XU6KBClFBP7cXTTqvkQEZQkhRS3+t4eVIhaKztZjhVeGEEJzWkyybSu+OX1R7BjXXJjYjxerNu0Wu37sJSwbvi9mLlottm2ZIbpYOgrXa1qhLaC82RWX3/tmwZUsoQleKrpbtBBf+fwjtru4iN23MkVMwFLxQb2awmH0t2Lewm/E+40qiQZOh0ViupcY17ifWHdXK6LX9BGW76wTsXcvPZsHj6SrzS6L2EubxSjbiqLtsHli+aZ1YpK9hejlfktIjxtDZ1tnibzt+pDE3WL0EHcRI2nFre3TxA8n0kTEws7CeqyXyK7iScK27bfiUpZW/D23o7B8c6yYtWChmPF+Y2HWeII4Fpk3fUZur6F8dbJGXP2roDJoRcTmcWLkkisiVRshFnepJrotuy7Cf50ipu2OFJrkQDH3TQvxxgK/fHVXGHL3M2UcGD11HF+Oq0fspTD2/WHCuAntyPawLKqgTVqCNiwjvGV/mlZQU89pKz6rBlPr2hpcT1nRw94MlXEL/jfRgeBlK9m+OW8wK1MKiFP1BLSErHHllFUP7M1UGLf4HxMdglm2ygdNASlUNd5jwkcP2LY+AI10gwOR9figeRhrXE9h1cMeM5UxLf43EYfgZazyyZOLkVGO9VgjjAzBoFIz+jo2oFytTgwZ+j4ffNqfFqkVaOM0loEDR9DTOppwncG7HpdXV1Ar01QtZZo6s3J2XbYOHE1w92m8b2mE+Wu9aV/bhGYDp+My5Xt+XfghGft34S23YMTiGXRJ+JNj19KQ4+NIqtLymQJjaUN0tdka/m7Sl9dtylG/z2eMHzqM4d1rcfN6FI+aTXe6VeStxseNYYjk68qoGVu57TiV8a8ZYWSUo7s2Msqx4cAA0zbD+HrqFH7YupYR7GXHWZEvfS7K5K2TeAxaFFAGbRAbloXTsn9TKqjr4bTVh1UfZ7Bt3TnSE0+xw/MSZj2G0cE0PV/dFYbcg1GVKWamgJ05Bm7bCGrgxGLLbE0XXdAmifh7CcTLccjUQVXWnIZVEoj75zYxaRLpj+qwbh3M064Tcy8eYZk3mJXuSDoFIxFzO4Y06d/cqVvHnLSIB0/Ipxydxo3ArJc7e/u2J8F2CHXEeW7HpPE4m7rUMU8j4kEhrTEw+NejBrUa9b9XV6FSCYQoKHjXw1I8IWiXZcfuOFR05ejJUFy6tKdC9gX/9bYp37QJ1nIgWXIGt/9cjecdJyb1sGOuv0Dw2MMn27bCefBIMbraLIIHwoDc2akR8uPZnYLTFVBvFfux/JAW1+9m06f5UkZt86Jgx8YcGNlgY2XAxXJ9WH7IIEf6o8xvn+N3OuukgDJI8dxLiEeOk6GOirLmDakSe5R78YJaDoMZmt0wSJKE+pO8dff2f5qse6dTBRu05w/QYt7Mhw1blEGbjLBr34yoGd/j3n8j42xusHn9VRw/6UxHeRZe/in06myCNjoWgy7v8F77DBZ9nTeY1RjayQIhy//e8rIQyPLD/+QEgnwjqdapNebq7Gu26twReZYX/im96GyiJTrWgC69O1Imb9ocqBsNZ2zrtrjMsWXLITMwakXnjjKzvPxJ6dUZE200sQZd6N2xDGQAIvtBoipfgXLp90lIByk5gpsPtNhkFabOCgreNYaOZQsO2jWm2QVW7a7KnMM/4PKWMz90P8lce0BkkvnQwTYrMoq0Tl1pc3EFvY+bs+nH16hwcDkaWSYzPQMdxf9PDx6jVrrarDcdy8CBJ5TySenI067ZZuzFM6wLs3b2ZdDCnvTZHsC0TuVIv59AOhLJETd5oLUhC8h1HkfqJa6kdaN3wyN4/pMzvR/z7R97DcV5L+c7HXWis+8ysqN9syhmfO9O/43jsLmxmfVXW/KabSjTJi/i9fUTaZd5AjcvGesKIk/d/bdg80w6PSKDC+GGDHyvDcb5v3wxxO/j+xVlmbF1Np2r5xyZG2DSrD02N3fy3Rdfs9gric6TvuDt+i3pZBvLpnlrOBcVTsDVKoz8dgwd7O1pGLOHuV+5MG9LEJajvmJwjVscWevGht+jMG7cjJray+xatYHfo4xp3Kwh9cQhnPsuJv3dT+hQRQUYYNy0E7axm5i35hxR4QFcrTKSb8e0QIR6sdbtcVoby8qPn3IGJjSoEsWF8p/weefqqAyMadrJlthN81hzLorwgKtUGfktY5pJBHu447b3GhVee4vudjZkXVzINwuPEaqqQfmbl4hVVSTp0j72B8rYOTYl6/RW1uwORt3KgYbJx/h17UHCjDvyzqcDeS0uT3kbPvR1rdCUDg1j2DP3K1zmbSHIchRfvZPKr6MmEeAwhVGv10PyX8LX7oFUad+SrOMb+SNaIi3Kn70nDRg853M61Mri6qa5LD4YSrKJAdEn/yLNui6Jf2xmd7AhLR3r8+DYFtYdvkFlh47w6xcsvaIhLS4eo/YD6dYwgZ3uK9kbWh77fk4M63gvX5vVveXJajcPgg1b4lj/Ace2rOPwjcq88fYb1K2owsC4qc62biFC8crRrg1tLKlsCOLBSb7/dClXNGnExRvRfuBw3miu4uLCb1h4LBRVjfLcvBRLeTt73qyv4vI+D05ejyTIJ5wGn89iYPUA5uRJ36GumvBDS1hzIgvbXu3I2jMvV50kVMri6iEvQvKWoXsvendtwM2d3/HF14vxSurMpC/60sWhITF75vKVyzy2BFkyampvIhc65aq77h2s/lM2Onc6SVd/ottXldmx14kaL8oD1OoAAAC1SURBVGmlVk66TQwWWJqW3qXgEo0UhmuXnkR8F4Rb1wLOgVIocehUS6KPN0GGJpR/iVpSmVoqYi1WJCRZRir1GzlKFzoVU9FxPCu/6v3yhsMKxUwmN8+cItG6LUZBp7meWtz2KBQWZfO/goIeoYxJFRT0CEWwCgp6hCJYBQU9QhGsgoIeoQhWQUGPUASroKBHKIJVUNAjFMEqKOgRimAVFPQIRbAKCnqEIlgFBT1CEayCgh7xf6n4/D6txQJkAAAAAElFTkSuQmCC)
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid A cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
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)
If temperature of system increases, then fraction of solid submerged in liquid
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation
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)
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid A cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
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)
If temperature of system increases, then fraction of solid submerged in liquid
physics-General
physics-
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation
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)
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid A cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
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)
The relation between densities of solid and liquid at temperature T is
Solids and liquids both expand on heating. The density of substance decreases on expanding according to the relation
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)
when a solid is submerged in a liquid, liquid exerts an upward force on solid which is equal to the weight of liquid displaced by submerged part of solid. Solid will float or sink depends on relative densities of solid and liquid A cubical block of solid floats in a liquid with half of its volume submerged in liquid as shown in figure (at temperature T)
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)
The relation between densities of solid and liquid at temperature T is
physics-General
physics-
A cuboid ABCDEFGH is anisotropic with
,
. Coefficient of superficial expansion of faces can be
![](data:image/png;base64,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)
A cuboid ABCDEFGH is anisotropic with
,
. Coefficient of superficial expansion of faces can be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIMAAACCCAYAAABlwXvDAAAQ7UlEQVR4nO2de1BU5f/H39xcYEVuLiCmYppEJqZhiKaTWt6auBXaMEkyleNd0UYdMktDhkxHYMRwtURxhiiwQUXEtDIVkJsKiqCgoi4sLrflustenu8fvy/nGz8u7rKXc4DnNcMM59nnnPNm583zfJ7L+RwTQggBhQLAlG0BFO5AzUBhoGagMFAzUBioGSgM1AwUBmoGCgM1A4XBnK0b19XV4ebNmzA1NcWUKVMgEAhw9epVWFlZwcvLiy1ZQxrWWgY7OzskJSVh+/btEAgEAIBbt27BwsKCLUlDHtbMYGZmhn379qG8vBxlZWUAAJlMhqlTp7IlacjDaszg6OiITZs2ISoqCqWlpZg4cSKbcoY8JmwvVEmlUkyaNAkfffQRYmJiYG7OWhgz5GH9m7e1tUVYWBhMTU2pEViGE9++k5MT/P392ZYx5GHVDOnp6bCxsYFEIoGDgwObUihgOWaYNWsWxo8fD6FQCGtra6xfvx779u0Dn89nS9KQhtWWISsri/n9559/xuHDh2FhYYHo6GgWVQ1dWB9NAIBIJMLkyZMhlUphYmKCK1euYM6cOWzLGnJwYm1ix44dkEqlAABCCNasWcOyoqEJJ0YTVVVV4PF4UKvVsLe3R1VVFduShiScaBkAYP/+/TAzM8P+/fthasoZWUMKTsQMMTEx2LhxI6ytrVFUVIRz584hLCwMAPDLL7/A0tJyQM1DFBcXIyIiAi0tLZg7dy6USiWam5uxbt06jBkzhm15vUM4gFqtJoQQYmlpSe7fv88cE0KIj48PmTNnDlvS+s3OnTvJypUrmeMTJ04QgUBAJBIJi6r6hhPtsYmJSY/HBQUF+OCDD1BYWIiCggI2pPUbHo/X5XjRokWQSCQoLCxkSdGL4UQA2RvJycn49ttvIRaLERMTg5MnT7ItSSskEgkqKipQX1+P+Ph4+Pj4YO7cuWzL6hVOtAw9UVdXBzs7O1hbW2Pz5s1ISUmBWCxmW5ZWtLa2ori4GNeuXUNWVhYmTZoEhULBtqxe4awZjh8/DqVSiQMHDuD06dOYNm0a4uPj2ZalFW5ubvD390dYWBgKCwuRl5eHzZs3sy2rVzjZTRBCUFFRgR9//JEp8/T0xCeffILw8HAMGzaMRXX9w8rKCtOmTUNzczPbUnqFc2YghODEiRNwc3PrUj5jxgxIJBIIhUKsXbuW03MRarUalZWVqKqqQm5uLng8HlJSUpCVlYXMzEy25fUKJ+YZOrGyssI///zDTE3PmDEDtra2AICcnBy0tLQAAKZMmQJnZ2fWdL6Iu3fv4tmzZ13KXFxc4OHhwelWjTNmKCgogLe3N9zc3Dj9hemCXC7H+PHjcenSJbal9AgnzCAWi+Hl5QWxWIxjx45h9OjRbEvSO42NjVi9ejWam5vR0dHBtpweYd0Mcrkc77zzDtzd3ZGcnIyioiK88sorbErSOwqFAgsWLICtrS3+/vtvzgaRrEdha9asASEER44cYVuKwdiwYQPa29sRERHBtpQ+YXU0ERMTgwsXLiA/P7/b9O1gIT4+HmlpacjPz+dsi8DA0poIuXTpEuHz+SQnJ4cp61yoGixcuXKF8Pl8cv36dUIIIffu3SPDhw9nWVXvsGKGiooK4uDgQE6cONGlfDCZobKykggEAnL06FGmjOtmMHrM0NLSAj8/P4SEhCAkJMTYt+83hBCIxWK0trYCQJ8jgra2Nvj5+WH58uX4/PPPjSVRZ4waMxBCsGLFCowaNQr79+835q11IjExEWfOnMH8+fPB5/ORn58PAIiNje2xfmhoKOzt7XHw4EFjytQdYzZDu3btIhMmTCD19fU9fs7FbiIpKYl4enoSuVzOlJWXl5PQ0NAe6+/du5e4ubmR2trabp9xvZswmhlSU1PJiBEjyJ07d3qtwzUzqNVq4u7uTo4dO9bts+zs7G5lZ86cITY2NuT27ds9Xo+agRBSVFREbGxsSFpaWp/1uGaGJ0+eEAAkLy/vhXVLSkqIra0tSU1N7bUO182gcczQ2tqKlJQU5Ofnw9zcHAKBADKZDPPmzcPcuXNhZmbW43l1dXXw8/PDtm3b4Ovrq6/ezSh0roy+aK2koaEBvr6+2LhxIwIDA40hzTBo45zW1lZiZmZGysrKCCGE1NbWkpCQEPLWW2+Rurq6bvUVCgWZP38+CQoK0uj6XGsZ1Go1GTlyJDl58mSvdZRKJVm4cCHx9/fvspG3J7jeMmg1tLS2toa5uTnTCjg6OuL48eNwdHTEunXrutXfvHkz6urqkJCQoB/nGhkTExOsXr0acXFxkMvlXT47f/481Go1tm3bhqqqKiQmJnbb2DvQ0HloaWpqipCQEAQHByMuLo55tP7YsWP49ddfkZeXB2tra52FssXu3bthZWWFefPm4cMPP4S1tTVMTU2xdOlSnDp1CgkJCcjLy8Pw4cPZlqozeplnGDNmDAghaGlpgYODA7KysrBhwwZERESgrKyMSeD1IlQqFa5du4ZHjx7pQ5be8PLygqenJyQSCSwsLODk5ITff/8d27dvx7lz5/Dyyy+zLVEv6MUMlZWVsLGxgaurKwCgpqYGAoEAQqFQq9Q8SqUSe/fuHRCLVk1NTXB2dsaCBQvYlqI/tA0yeDweKS8vZ47VajVZtGgR2bBhQ5d6w4YNYwJNTeFaANkXd+/eJSNGjNDqnEEVQLa1tUGhUKCpqQlKpRJ3795FUFAQbGxsEBUVZSi/UoyEVvMM58+fx+7du5Geno7MzEyMHDkSERERcHd3H/CRNEULM/D5fAQFBRlSC4VlWN/2RuEO1AwUBmoGCgM1A4WBmoHCQM1AYaBmoDBQM1AYqBkoDNQMFAbOZW7pRKlU9pgMy8zMbNDmb2AbzpqhsbERUVFROHz4MPMwSmlpKZqamvDTTz+xrE6/NDY24uDBg1CpVLC0tISVlRXMzMyMnwzMUGvj+tjPUFRUROzt7bvUycjI0Is+XdHXfgaRSERmzZpFHjx4wJSVlJQQHx8fvejUhgEVM9y/fx+LFy9mW4Ze2bp1K3x9fbu8xtHDwwO7du0yuhbOdhOdyGQyHD16FK2trbh9+zaOHz/OtiS9IZVKcfr0aWzdupUpUyqVaG1thY+PD6RSKZPgzBhwvmXg8XgIDg7GihUrMG7cOLbl6JXa2lp0dHR02fMpl8tx9uxZ2NnZIT093ah6OG8GExMT8Pl8ODo6cjq7an8YO3YseDwe8vLymDI+n4+AgAAAwJIlS4yqh9NmIP8v95idnR1LSgyDhYUFPvvsMyQkJHT7W4Hu2fYNDWfNIJFIkJKSgvb2dmRmZkImk7EtySDs3bsXlpaW+OKLL1BZWQkAqK6uZoaX/0atVuPIkSMIDw9HeHg44uPjoVKpul2zvLwccXFxSEhIgEKhwIULFyAUCplEI71iqGGKrkNLpVJJOjo6mJ8XPcdobPS9Vb64uJjExsaS2NhYkpaWRqqrq3us19DQQJYtW0YAEADkzTff7DEFwOHDh8mUKVOIQqEg33//PSkpKXmhPoPlgeTxeCguLsakSZM0qp+dnY3g4GC4uLjAwsLCEJL0SufoZtasWRqfU1tbiydPnmD69Ok637+6uhrl5eUA/q+72bNnD3bs2MF8TghBYGAgVCoVNm3apNHDPpwYWj59+hQBAQF4//338e6777ItRyOePXuGe/fuafzaxYaGBnz11VcIDAzUOTCsqanBoUOHmOM5c+Zg2bJlXeqYmJjgyy+/xOLFi7sMXftEi1ZOKzTtJtra2sj06dPJqlWrDCXFIGjTTchkMuLt7d1r6h9tSExMJDY2NgQAsbW1JUKhsMd6bW1tJCoqily+fJm4uLiQqqqqF16bdTN8/PHH5O233yYdHR2GkmIQtDHDypUrycyZM4lMJtPpniqVijx9+pT5aWpq6rGeVColwcHBpKSkhHR0dJD33nuPLF68mDx58qTP67NqhsjISDJ27Fjy/PlzQ8kwGJqa4eDBg8TV1VWj/0x9IZPJiEgkIlKplCgUCiISiYhIJOo1sVonrJnh7NmzZPjw4aSwsNBQEgyKJmb4448/CJ/PJ7m5uUZSpRusmKEzGVZycrKhbm9wXmSGziy4faUA4hpGn3RqbGyEn58f1q9f3y0CHiy0tLTA19cXn376KVasWMG2HI0xqhlUKhWWL18ODw8PfPfdd8a8tdEg/82C6+rqih9++IFtOVqh9TzDrVu3EB0dDSsrK7i7uwMA6uvr4eTkhPXr1/d57rZt2yASiZCdnT1oH+H/5ptvcOfOHeTm5vaaDpGraG2GN954A/b29lAoFF1WEaOjo/s87+TJk0hISEBubi5sbGy0VzoASE1NRUxMDLKzs2Fvb8+2HK3p1wykpaVll82qjY2NfbYKN27cwNq1a5GWloYJEyb055acp6ioCKGhoTh16hRee+01tuX0i37HDHK5HFKpFBKJBEeOHOk1kVdVVRUCAgIQGRk5uJJh/YuBnAX33/TbDA8fPsTp06eRkpKCjIyMHuvI5XIEBARgyZIl2LhxY79FchmlUomgoCDMmDEDO3fuZFuOTvR7ocrDwwOhoaEAgNmzZ/dY5+uvv4a5uXmX1xgPNsLCwlBfX49z586xLUVn9LJq6enpicbGRjx//pxZslapVMjJycGtW7cG7UMvHR0dSE5OHvBZcDvplxkaGhogkUhQU1MDU1NTqFQqhIeH4+jRowCAzMxMqFQqbN26FSKRCCKRSK+iuUBGRgZkMhkyMzMHzUZdrTe3FBQUoKysrNuePTc3N8yePRsPHjyAt7c3xo0bB7FY3OPevsGATCbD+PHjcfPmTZSWluLy5ctQq9Vwd3fHwoULUVlZiYyMDCgUCowbNw5Lly7VKlsuK+hzblsqlZJXX32VbN++XZ+XHRBERkaS119/vcv2vMTEROLg4EAUCgWLyjRHb9PRarUawcHBmDBhAiIjI/V12QGDs7MzXF1du8ysOjk5wcXFhfstwn/Rm8rw8HA8fPgQOTk5zBtcKAMLvZghKSkJQqEQN27cwIgRI/RxyQHJ48ePceDAAeZY01crcAWdzVBQUIBVq1YhNTV10L3dXlvc3Ny6bD69ePEirl+/zqIi7dCpPa+pqYG/vz92796NhQsX6ksThSX6bYaOjg4EBgZi/vz52LJliz41DUja29s1KuMyWpnh3yuVa9euhUqlglAo1LuogUZ5eTnEYjEmTpyIv/76C8D/nquYOXMmLly4AKVSybJKDdB0DKpWq8mWLVsIIYTExsYafccvxfBoHEDu2bMHly5dwuXLlxEeHo4///wTo0aNMqRPKUZGo+no7OxszJ49G9OnT8ejR48QHR2NpUuXor29HS+99JIxdFKMgEYxw82bN0EIwf379+Hu7o64uDgsWbKEeYclZXCgUTfRuerY3NyM7OxsjB49Grm5uYNi2ZbyP7Qyg52dHbO9y9XVFUqlEqWlpV3qOjs7QyAQ6F8pxeBo1E14e3sjPT0dNTU1SEhIYDZ8NjQ0IDExEdXV1bh48SKmTZuGiooKgwqmGA6dknXIZDLIZDIMGzYMXl5eWL169aDd6zgU0EvmllWrVqGpqQlJSUmD9uGYoYDOC1W//fYbrl69iry8PJiYmKC6uprOPwxQdFqoevz4MdatW4dDhw6hubkZjx8/RkpKir60UYyMTt1EUVER7ty506Vs6tSpmDx5ss7CKMbHYNneKAMPuj+NwkDNQGGgZqAwUDNQGKgZKAzUDBQGagYKAzUDhYGagcJAzUBhoGagMFAzUBioGSgM1AwUBmoGCgM1A4WBmoHC8B9lzTXjqBsIQAAAAABJRU5ErkJggg==)
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-
A rod of length 2m rests on smooth horizontal floor. If the rod is heated from 0°C to 20°C. Find the longitudinal strain developed? ![open parentheses alpha equals 5 cross times 10 to the power of negative 5 end exponent divided by blank to the power of ring operator end exponent C close parentheses](data:image/png;base64,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)
A rod of length 2m rests on smooth horizontal floor. If the rod is heated from 0°C to 20°C. Find the longitudinal strain developed? ![open parentheses alpha equals 5 cross times 10 to the power of negative 5 end exponent divided by blank to the power of ring operator end exponent C close parentheses](data:image/png;base64,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)
physics-General
physics-
A metallic wire of length L is fixed between two rigid supports. If the wire is cooled through a temperature difference
(Y = young’s modulus,
= density,
= coefficient of linear expansion) then the frequency of transverse vibration is proportional to :
A metallic wire of length L is fixed between two rigid supports. If the wire is cooled through a temperature difference
(Y = young’s modulus,
= density,
= coefficient of linear expansion) then the frequency of transverse vibration is proportional to :
physics-General
physics-
A light ray gets reflected from a pair of mutually perpendicular mirrors, not necessarily along axes. The intersection point of mirrors is at origin. The incident light is along y = x + 2. If the light ray strikes both mirrors in succession, then it may get reflected finally along the line:
![](data:image/png;base64,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)
A light ray gets reflected from a pair of mutually perpendicular mirrors, not necessarily along axes. The intersection point of mirrors is at origin. The incident light is along y = x + 2. If the light ray strikes both mirrors in succession, then it may get reflected finally along the line:
![](data:image/png;base64,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)
physics-General
physics-
A glass prism of refractive index 1.5 is immersed in water (
= 4/3). Light beam incident normally on the face AB is totally reflected to reach the face BC if
![](data:image/png;base64,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)
A glass prism of refractive index 1.5 is immersed in water (
= 4/3). Light beam incident normally on the face AB is totally reflected to reach the face BC if
![](data:image/png;base64,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)
physics-General
physics-
A slab of high quality flat glass, with parallel faces, is placed in the path of a parallel light beam before it is focussed to a spot by a lens. The glass is rotated slightly back and forth from the vertical orientation, about an axis out of the page as shown in the figure. According to ray optics the effect on the focussed spot is:
![](data:image/png;base64,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)
A slab of high quality flat glass, with parallel faces, is placed in the path of a parallel light beam before it is focussed to a spot by a lens. The glass is rotated slightly back and forth from the vertical orientation, about an axis out of the page as shown in the figure. According to ray optics the effect on the focussed spot is:
![](data:image/png;base64,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)
physics-General
physics-
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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)
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
![](data:image/png;base64,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)
physics-General
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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)
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