Maths-
General
Easy
Question
If
is a non-zero number and
, then f(x) is:
The correct answer is: ![fraction numerator x to the power of 4 m end exponent over denominator 2 m left parenthesis x to the power of 2 m end exponent plus x to the power of m end exponent plus 1 right parenthesis to the power of 2 end exponent end fraction](data:image/png;base64,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)
I ![equals not stretchy integral subscript blank superscript blank fraction numerator x to the power of 5 m minus 1 end exponent plus 2 x to the power of 4 m minus 1 end exponent over denominator x to the power of 6 m end exponent left parenthesis 1 plus x to the power of negative m end exponent plus x to the power of negative 2 m end exponent right parenthesis to the power of 3 end exponent end fraction d x](data:image/png;base64,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)
Put ![1 plus x to the power of negative m end exponent plus x to the power of negative 2 m end exponent equals r](data:image/png;base64,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)
-m ![x to the power of negative m minus l end exponent plus negative 2 m x to the power of negative 2 m minus 1 end exponent d x equals d r](data:image/png;base64,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)
![rightwards double arrow left parenthesis x to the power of negative m end exponent plus 2 x to the power of 2 m minus 1 end exponent right parenthesis d x equals fraction numerator negative 1 over denominator m end fraction d r rightwards double arrow fraction numerator negative 1 over denominator m end fraction not stretchy integral subscript blank superscript blank fraction numerator 1 over denominator r to the power of 3 end exponent end fraction d r](data:image/png;base64,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)
![equals fraction numerator negative 1 over denominator m end fraction left square bracket fraction numerator 1 over denominator 2 t to the power of 2 end exponent end fraction right square bracket equals fraction numerator 1 over denominator 2 m end fraction left parenthesis fraction numerator 1 over denominator left parenthesis 1 plus x to the power of negative m end exponent plus x to the power of negative 2 m end exponent right parenthesis to the power of 2 end exponent end fraction right parenthesis](data:image/png;base64,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)
![equals fraction numerator x to the power of 4 m end exponent over denominator 2 m left parenthesis x to the power of 2 m end exponent plus x to the power of m end exponent plus 1 right parenthesis to the power of 2 end exponent end fraction](data:image/png;base64,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)
Related Questions to study
Maths-
The integral
equal
The integral
equal
Maths-General
Maths-
If
log
f(x)
then
![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
If
log
f(x)
then
![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
Maths-General
Maths-
An incomplete frequency distribution is given below Median value is 46, the missing frequency is
![](data:image/png;base64,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)
An incomplete frequency distribution is given below Median value is 46, the missing frequency is
![](data:image/png;base64,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)
Maths-General
Physics-
In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP
![](data:image/png;base64,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)
In the adjacent diagram, CP represents a wave front and AO & BP, the corresponding two rays. Find the condition on q for constructive interference at P between the ray BP and reflected ray OP
![](data:image/png;base64,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)
Physics-General
Physics-
A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be
![](data:image/png;base64,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)
A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The observed interference fringes from this combination shall be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAAB7CAYAAAASXZ6QAAAP/klEQVR4nO2dbVfa2NeHf3kkCc9JBJRarW2dzrzp9/8Is1anj87Uh1pRQFQQJAQIAuF+0f/JjQoKFgORfa3FolN0rdMMV87J3vvsww0GgwEIgnhS+HkPgCCWARKNIHyARCMIHyDRCMIHSDSC8AESjSB8gEQjCB8g0QjCB0g0gvABEo0gfIBEIwgfINEIwgdINILwARKNIHyARCMIHyDRCMIHSDSC8AESjSB8gEQjCB8g0QjCB0g0gvABEo0gfIBEIwgfINEIwgdINILwARKNIHyARCMIHxDnPYBlYjAYoNfroVarYWdnB9Vqdd5DehQ8z0OWZaytreH9+/cQBGHeQ1p4SDSfcBwH1WoVu7u7ODg4QLfbnfeQpkYQBKiqCl3X8fbtW0QikXkPKTCQaE+M4zg4Pz/HyckJdnd30el05j2kqREEAZFIBMlkEpubm55gHMeB47g5jy4YkGhPhOM4KBaLKJVK+P79eyAF43ke0WgUpmlidXUVsVgMPM/f+Hz4v4nxkGgzptPp4OTkBMViEUdHR2g2m/Me0qOIxWJYXV2FYRhIJBIjhRJF+vpMCl2pGdHtdpHP53F4eIhSqYRGo4EgnvEYDoexubmJeDw+VjDg17JRVVWfRxdcSLTfxHVdHB4eYn9/H5eXl7BtG67rzntYU6NpGl69eoVkMnlniTgKFhghJoNE+w12dnZwcHCAarUKx3ECOYMpioLNzU1kMhmoqjpRqH4wGCAUCtHz2RSQaI9gf38fX79+Rblchuu6gRRMkiS8fPkSW1tbkGV5oujh8L8zmUw+5fCeHSTaBLBEc6FQwOfPn3F2doZ+vz/vYU0Nx3EQRRGZTAZ//vknZFme6PeGBRsMBlBVlQIhU0JX6x4GgwHa7TYqlQq+fv2K09NTXF9fz3tYUyMIAkKhEJLJJP766y+EQqGJf5dJxt5d14WqqrBt+0nGGnREUUQoFLqzQuAGQVz3+IBlWajX6/j27RuKxWIg82CSJEHTNJimifX1dYTD4YkTzLcFGwwGGAwGqFQq3pKZ+H9EUUQ0GkUymcT29vadmxnNaLeo1+u4vLzE3t4eisUiHMeZ95CmRhAExONxL9EcDocnDlzcXiYOvxqNBvb392FZ1lMNPXCIoohYLAbDMGAYBsLh8MibEIn2PxqNBk5PT5HL5VAsFtFqteY9pEdhmiYMw0A6nUYkEplasNszGHtdX1+jUCgENgE/aziO85L6qVQK0Wj03tXC0ovWbrdxdHSEfD6PUqmEVqsVyGWRaZpYWVnBysoKwuHwxGH6238efhYbFu3i4gKVSiWQ12bWqKqKdDqNdDoNwzDu3MxGXfulFc11XXz//h3Hx8c4Pz9Hu90O5JdI13Wsrq7CNE1omvagYLcfyUcJxt6ZZOVyGcfHx2i324FMZcyKUCiEbDbrlaVJknRHslF/ByypaN+/f8fBwQHK5TI6nU4gBYvFYnj58iVM05wo0XyfYPe9rq6ukMvl0Gq1llYytvcunU4jkUhAFMU7y0RRFJFIJBAKhWhG+/HjB759+4aLiwv0er1AfnEURcGbN2+QTqcnqs4YJxhwd3k4/HJdF61WC0dHR4Gt25wFpmlia2sLuq5DEIQ7grHAEws4jXtOe/aiua6L09NT/PPPPyiVSuj1evMe0tSwfV/v3r1DNpudOA826hkMeFgwAGg2m/jvv/+WMvjBAh1v376FaZojk/Nsj148Hp8o4PRsRWM7mj9//oxCoRDYRLMkSdjY2MD6+joURZno9+4TjL2PEoxVwLRaLfz777+BvGa/gyRJUFUVr1+/RiqVgiRJNz7nOM4rpk4kElO1cHh2otm2jUajgS9fvqBQKAQyDyaKohfZevHixcSJ5t8RrN/vw3EcWJaFo6OjQLZaeCyhUAiqqmJjYwPpdPpOaRrHcZAkCaFQaGrBGM9GtEajgWq1ir29PeTzebTb7XkPaWoEQfCSn2traxPnwcaF6R96ua6Lfr+PTqeDRqOBSqWCer2+NJKFQiFEo1Gsrq4inU7fWTGw2lBZlhGPxyeuDR1F4EWzbRtnZ2fI5XJeQjWID+66rkPXdWQyGUSj0ZnnwYZf/X4fruvi+voalmWhVqvh6uoK19fXgbx20yLLMpLJJFKpFFZWVqCq6sgooqIoUFUViqL8dqevwIrmOA6Oj4+Rz+dRLBbRbDYDGabXdR2maXrVBdOE6Uf9+aFlYr/fR7fbhWVZqFarsCwrsHvppoXneaTTaZim6aVFRiWbNU2DoiheqH4WDYgCJ9pgMMDe3h5OTk5QKpUCK1gikUAmk8HKygoikYgvgvX7fViWhfPzczSbzaURDIBXKmUYBhRFGbkk1zQN4XDY+3yWHb4CVb1fKBSwv7+Ps7MzOI4TSME0TUMmk4FpmhOVSt0n2H3h+eEgR6/XQ6PR8ErMOp3O0giWTqeRzWah6zpkWR4pmKqqiEQiM53BbhOoGY0teRRFmTjUvUhEIhFsbGxMvaP5thTjZq3hz3q9Hvr9PprNJkqlEur1emCT9I9B13W8evXKE2zU9VYUBdFo9ElmsNsESjRFUWCaJur1+ryHMjWqquKPP/4Az/MPBh3uE4y9jxOt1+uh1+vBcRycnp7i8vIykLvBH0skEsH29jZSqdTYXeCSJCGRSIx8RnsqAiUayy8FbcnIcRwMw4AkSffOKo8VjC0Ru90uHMfBxcUFLi4ulkYwtqv5zZs3yGQydxLNwK9ACCuX0jTN98ZCgRKNXaygwXEcZFm+MfMMM0mimb0Py+W6rhemb7fbqFarOD8/D2SZ2WOQZRmKomBjYwOrq6sj81w8z3u7nyfZ3fBUBEq0UfmOIMBxnFef+FD08KEE87BgnU4HzWYT9Xod5XJ5aUqmBEFANBpFNpv12uSN+hnWykHTtLk3EwqUaKIoQhAECIIQqGWRLMsQRdETZNpEM5vRhhPNjUYD9XodtVptacL0rHLGNE1kMhnEYrE7N16e572SKtataxFuzoESjS0Vms1moERjFd69Xm+saOMqOZicrut6UddarQbLspZmI+Zw2wDDMEZWzLMW5ayaY1EEYwRKNOBXb/irq6t5D2MqFEWB67o3AiEPJZqHBWN5sHK5DNu2l0Yw4FcUkZ0FMG5LiqZpnmSLJhgjUKK1Wi0Ui8W5r7enQdd1SJJ04xlrmkQzq+VctkqOcDiM169fI5FIjC2uVlXVq+R4qkTzrAjEN9ZxHOzu7iKXy6FSqeD9+/eQJCkQVebs0L5Op4N+v/9goIMJ1mw2cXZ2BsuylqbYF/glz9bWFlKp1Ng8F6u6D4JgjIUX7eDgwOtzz57LisUistnswovG9jaxKo2H8mAs0VwqlXB5ebk0YXrg1/P35uYmNjc3IUnSSHkkSUI8Hp/4MI5FYiFF63a7qFQq+PjxI4rF4p2wdaVSwYsXLxY6+qgoipc7GzWb3U40dzodlMvlpcqDsQ2Va2tr2N7eHpkH4zgOPM8jkUjMNQ/2uyyUaK1WC41GA58+fUI+nx/bhrvb7eL8/BymaS6kaOyLwZa3LAhyu5qeJZqvrq4C28/kMQiCAEVRoOs63r17N7IHyvCmS9YYJ8gshGi2bcOyLOzs7Ey0O9p1XViW5UWhFqkki+d5xONxhEIhrz0AuxkM58GGE81B7Ov/GARBQDgcRjKZxNbWFsLh8J2fGW4bEIvFRpZTBZG5imbbNiqVCg4PD3FycjJxx6XB4Fe/wVAohFQqBY7jFiJYwHI5mqZhMBh4kg0LZtu2l2heljA9uy4rKytYX19HPB6/e9rK/wRTFAXhcHjiHQ5BYS6itdttFItFnJycIJ/Pw7btqb9w/X4fV1dXiEajCIfDc192sTKraDQKnufR6XTQ7Xa9Z7BarYZGowHLspaqGSnbccFalo9aJsqyfGNX83MSjOGraL1eD4eHhygUCigWi7993rPjOCiXyxBFEZIkzW0JOSyZIAjodDqeaJeXl94RUNfX1wu1zH1KZFlGJpOBruswDGNks1d2Eossy89WMIZvou3t7eH4+Njb5TuLIIbruqjX6+A4DplMBqIozmWmYMsdURThOI7XU5L15Oh2u0sjGAC8ePECqVRq7K5mJlgoFHp2S8RxPHkrg58/f2J3dxelUunJ+tyzKN/q6qrv0alwOOz1XXQcB5eXl7i4uECj0ViqRDMAGIbhnQcw6rAHVhTMqumXQTDGk4lWKBTw5csX7zjap/7CcRwHTdOwsbHhbUt/yv+RPM8jGo16ubJarYaTkxNYlrVULQMAIBqN4s2bNzBNc+QMxfM8IpEIYrFYYCo5Zs1MRev3+6hWq/jw4QPy+fxc9kdJkgTTNBGPx70tNbMmFAp55T+dTgc/fvxArVabe0DGT9h2lO3t7Xt3NWuahmQyGfg82O8yE9Ecx0Gz2cTHjx9xfHw89zbcHMdB13UvTCyKordUeczdlP0OS6ACv1IMx8fHqFQqC18KNkskSYIkSdja2sLa2trIag52OL1hGEsvGOO3RGs2m7BtGzs7O8jlcgvXhpvtxFVV1Wslxh7OmXT3icc+F0URPM97ObFKpYJKpTL3G4qfyLIMVVWRzWaxtrY2sn0229UciURm0t33OfEo0brdLsrlMvb395HL5WDb9lOMbWawU0IkSfJSAWym43n+jnjs75hc3W4X7XYblmXBtu2l6osoSRJisRhSqRQymQw0TRvZPns4FxakbUx+MZVovV4PFxcXyOfzODo6QrVaDVTYmlUfSJLkPb8NLy2H78Ddbhccx6HVaqHdbgf26N3HIgjCjXbl7KC9YXiev7GreVkDHZMwkWiDwa/Dwvf3970tHItYzDstbFkoCII3q7Gi3263O7Zr1XMnlUp5lRyjBAPg9eRgFfUk2P08KFqtVsOnT59QLpdRrVafhWDEaFZWVpDJZGAYxtjeh0yuRW4bsIiMXUzX63V8+PDB2+VLgj1fkskk1tfXYRjGvbuaWZCDBJueO6LZto2PHz/i58+faLVaS7l0WhYikQi2tra8Yt9RgrFgCD2D/R43lo65XA5///330jTiXFYEQUA2mx3b3Zf9TCKRGPuMRkyHN6O5rgtRFJFIJJYqP7RsiKKIly9fQtf1O4l2ltqIxWITndlGTM6NpSM7cX5ZckTLyObmJpLJ5A3J2JkGkUjE24VAzJYbM1q/3/d2uRLPk+ESMp7nvWQ+E4yewZ6GG7euwWBAF/uZY9s2ZFn2Nltqmja2vRsxO7xgiOu6aLfbS1VetKyIoui1wyPB/CFQZ1gTRFChuC1B+ACJRhA+QKIRhA+QaAThAyQaQfgAiUYQPkCiEYQPkGgE4QMkGkH4AIlGED5AohGED5BoBOEDJBpB+ACJRhA+QKIRhA+QaAThAyQaQfgAiUYQPkCiEYQPkGgE4QMkGkH4AIlGED5AohGED5BoBOEDJBpB+ACJRhA+QKIRhA+QaAThAyQaQfgAiUYQPkCiEYQPkGgE4QMkGkH4wP8B4Ny6/RRwKJcAAAAASUVORK5CYII=)
Physics-General
Physics-
A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio
is
![](data:image/png;base64,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)
A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in fig. It undergoes partial reflection and refraction. At each reflection 25% of incident energy is reflected. The rays AB and A'B' undergo interference. The ratio
is
![](data:image/png;base64,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)
Physics-General
Physics-
AB is incident wave front on mirror R and mirror S whereas PQ and
is reflected wave front from mirror R and mirror S respectively. Choose the correct statement
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)
AB is incident wave front on mirror R and mirror S whereas PQ and
is reflected wave front from mirror R and mirror S respectively. Choose the correct statement
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)
Physics-General
Physics-
In the diagram shown, the separation between the slit is equal to
where
is the wavelength of the light incident on the plane of the slits A thin film of thickness
and refractive index 2 has been placed in the front of the upper slit. Assuming
the distance of the central maxima on the screen from O is:
![](data:image/png;base64,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)
In the diagram shown, the separation between the slit is equal to
where
is the wavelength of the light incident on the plane of the slits A thin film of thickness
and refractive index 2 has been placed in the front of the upper slit. Assuming
the distance of the central maxima on the screen from O is:
![](data:image/png;base64,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)
Physics-General
Physics-
Three weight A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALIAAADTCAYAAAAlIkmXAAAgAElEQVR4nO2deVhTV974P2ENm2EHIYBLBUTEtSrgUrVKrYhWba2+2lo7daszaq0z1b7Tdqyd6bSO0trNunS09qmdVlu3iiuIO5tYHERlx7qwyCJbgCS/P/wlbxISFgUl4X6eJw/JvSf3nBs+OTn3e849R6RUKpUICBg5Zo+7AAICbYEgsoBJIIgsYBIIIguYBILIAiaBILKASSCILGASWDzuAjwMDQ0Nj7sIHRJzc3NEItHjLsYjxahFrqure9xF6JCIxWJBZGOitrb2cRehQ2JlZYWZWedqNRq1yNXV1Y+7CB0Se3v7x12ER45Ri1xRUfG4i9AhcXFxedxFeOQYtchlZWWPuwgdErlc/riL8MgRRDZBOmM0x6hFLi4uftxF6JB0RpFFwnjkB+P27dvU1tbi6uqKjY0NDQ0NlJaWUl5eTkBAwOMuXqejc8VoBEwWQWQBk0AQWcAkEEQWMAkEkQVMAkFkAZNAEFnAJBBEFjAJBJEFTAJBZAGTQBBZwCQQRBYwCQSRBUwCQWQBk0AQWcAkMOqB9Y+a+vp6MjIySE5OxsnJiX79+jVKc+vWLT755BPs7e3p3r07ffr0wdfXF29vbywtLR9DqTsHgsgtIC0tjUOHDnHs2DFqa2sZPHgwYWFhetOKxWJ69+5NQUEBu3fvZtOmTfj4+NCrVy9GjBhBYGAgvXv3fsRnYPoId4gYoLq6mvj4eP7xj39QXFxMVFQUU6dOZdCgQYhEIu7cuaP3DpGysjL1HSJKpZLr16+zb98+du3aRXFxMUOGDOHJJ59k5MiRhISEYGtr+5jP1DQQRNZAqVRSU1PD5cuXef/998nKyuLdd99l+vTpmJubq9MALRIZ0Jrx5/Tp0yxYsID6+npCQ0Pp168fY8eOJTAwECsrq043O1BbIjQt/j9yuZzc3Fx+/PFHkpKSCAkJobKykp49eyISiXjQ77vm+wICAnBzc2PMmDEkJiby66+/kpWVxciRIwkPD6dr167qL4xA6xBEBhQKBRcvXmTnzp1UVFSwYsUKQkND+eSTT/juu+8IDg7G2tpaS8qmxNa3T6FQsH79egYPHsw777xDfn4+69evJy0tjYqKCkpKShg5ciS9e/cWZH4AhPAbcOLECbZu3Yq7uztr164lNDQUpVLJ3LlzycnJIT4+Xi2nUqlstnZWpdFMl5ycTGJiIq+//jpKpRJfX1/ee+89Zs+eTXl5OfHx8ezbt49Lly51yglWHpZOXyP/+uuvfPbZZ7zyyitERETg4OCgFtDBwYFFixbxt7/9jUGDBiGRSIDmZVYoFADqJklZWRkbN27k5Zdfxs/PT30MiUTCjBkz8PHx4ZNPPiEpKQkzMzMqKysJCwvDwqLT/3taTKeukU+fPs1XX33F/PnzmTp1Kg4ODoC2qE899RS9e/dmy5YtKJVKFApFsyKr9qvSHjp0CGtrayIiIhrV1jY2NowZM4Y///nP1NXV8dtvv3H27FnOnz/f/h+ACdFpRU5PT+f999/nf/7nf4iKilJPw6rbDjY3N+edd97hp59+IiUlBYVCoa5x9aESWPW4fv06R48eZc6cOTg6OmpJrPorEokIDw9n+fLlpKamkpWVRUJCAhcvXmzHT8C06JQi5+fn8+677zJu3DiioqLUYS/ddrCqRvX09GTOnDmsW7dOa7shVBIrlUoOHDhAt27dCAwMVDc1dB9wX+aRI0fy9ttvc/DgQW7cuEFycjKFhYXt/4GYAJ1S5I0bN5KUlMSQIUOwtrYGDEuskvLFF1/E0tKSEydONFkrK5VK5HI5crmchIQEMjMzGTduHBKJRKtZok9mCwsLIiIisLGx4fjx49y6dYvExMRH86EYOZ1O5MuXL1NcXMzLL7/M/Pnz+eMf/0hJSYnWMg6aMqvks7GxYc6cOXz22WfcvHmz2Rq5srKSQ4cOIZVK6dWrV6Pjab6/oaGBiooKtm3bRnh4ODNnzkQsFpOTk0NmZiZpaWkPHMfuLHQqkWUyGSdOnKB379788Y9/JCkpCQ8PDyZPnsy///1v8vLykMlkjS7qVLVvr1696N69O/v27Wtyxsv6+nrOnz/PvXv3GDNmDHZ2do2Op1QqaWhooLi4mCNHjrB06VISExPZtWsXa9asYcmSJWRnZ1NYWEhmZiZVVVWP6mMySszfe++99x53IR4VFy9eJD4+ngkTJuDv74+VlRUjR44kNDSUvXv3Ehsbi7m5Ofb29ojFYgAt8cRiMba2tpw7dw5PT09cXFywtbXF0tIShUJBbW0t1dXVVFVVsXfvXqRSKePGjdN7IVlZWcmFCxf48ccfuXjxIuPHj+f111/H19cXkUhE165dOXPmDKWlpTg4OODm5oarq6vQjW2ATiOyTCbj8OHDKJVKJk6cqBYVwM3NjZEjR6JQKEhKSiI1NZV79+7h6empllQloZ2dHbm5ueTn59O/f/9GIldUVJCamkp2djbTp0/HyclJqxxKpZJLly5x4MABzp49i6enJwsWLCA0NFRrvIWVlRVKpZITJ07g4uKCk5OTMBS0CTpNxL2oqIhbt27Rp08frY4NuN+mtbOzY9q0aYSGhvLLL78QFxfHtWvXGDJkCAMHDkQkEqFQKLC3t2fw4MHcvHlTbz53797lxIkThIeHI5VKtTpHCgoKiI2N5erVq7i5ufHSSy/Rt2/fRt3fIpEIS0tLgoODcXFxobS0lPz8fMrKyrCxsWnnT8o46TQi37x5k/LycgIDA7W268aNPTw8mDNnDpmZmVy8eJEtW7bg4+PDggUL6NKlCwqFgoCAALy8vPTmU19fj4WFBWFhYcjlcpRKJeXl5cTFxREbG4tUKiUqKoqQkBCcnZ3VITnNJoPqtZubG0FBQVy/fp3CwkLKysrw9PQUmhd66BQi19fXk5OTg7m5OT179gQaC6z5sLa2pnfv3vj6+uLv78/+/fuZN28es2fPJjIyEktLS4M1o6OjI5MmTcLBwQG5XE5ycjLbtm3DxcWFGTNmEBAQQNeuXTEzM1MLq8pXV1AnJycCAwM5f/48VVVV3Lp1i+7du2s1iwTu0ylELi8vJzs7m8DAQHXcWEVTQovFYkJCQpBKpURGRrJ161b+85//8PrrrxMUFKQ3LxsbGwIDA8nPz2fXrl3k5+fz9NNPM2LECKRSKebm5igUCr0C68psYWFBt27dkEgklJeXU1ZWRn19vSCyHjqFyDKZjMrKSgYNGqS1valhmZpCd+nShcDAQFavXk1cXBybN28mLCyMl156qVFetbW1HDlyhP379xMcHMzKlSvx8/PD0tLSYEeIKj99zQxnZ2fc3Nyoq6ujtLSU+vr6tvpYTIpOIXJdXR1VVVU4Ozs3mU5XMN14sr29PRMmTCAkJIR79+6p09TU1KgfhYWF7N27l8WLFzNkyBD1Auf65NXM01C719bWFjs7O0pLSwWRm6BTdIjU19dTVVWFo6MjYLj2NbRNtxZ1d3fH19cXgOzsbObPn4+XlxcLFy5EJpPx6aef0r9//0Zd0i3NT7OMtra22NraUl9fT11dXZMDljoznaZGLi4uJjc3l6ysLL2C6o6tUD1XRR4aGhrU++RyOV5eXgQFBbFlyxYOHDhAQ0MDx48fRy6Xq+/xUz3MzMzUf/U9RCIRIpFI6zncD8NVV1eTl5dHTU0NSqWSGzdu4O7uLtxFokOnEFkul1NcXMylS5dIT09Xb9cVWvO5IcnlcjlFRUWMGDGCoKAgiouLkclkwP149G+//UZycjJ+fn74+flhbW3dSFZA/Ve1XVdgFQqFgoyMDDw8PGhoaGD9+vV88cUXjTpaOjudQmQzMzOkUimvvfaa1h0g+mpiuVyu9VdVEzc0NFBZWcnp06dJSkpCKpUC8MILL1BQUMC5c+fw9/dn6tSpVFdXU15ejlQqJSIiAqlUioWFhVYtbaiG1pRdJBJRU1PD+vXruXjxIubm5pw6dUr9xRH4PzqFyFZWVuoLJtVdICp075A2VDumpaVx5MgRysvLeeKJJ+jVqxcAI0eOxNXVlfT0dJydnfH29qaiooLff/+dlJQUNm3aRFhYGE8//TT29vaNLuo089LMT0V1dTUymQyxWIyNjY3QpDBAp7jYs7S0VIsMjWXRFzFQCXbnzh2++uorvvzyS1xcXJg5cyZRUVHk5OTwww8/kJubi5eXF4cPHyYoKIiUlBQOHjxIWFgYs2fPZvjw4Rw9epR3332XGzduaB1bV2B9QqtEtra2xt7eXriPzwCdQmQrKytkMhnJyckG0+jK1dDQwP79+5k/fz7l5eWsWrWK559/Hn9/f0pKSkhMTEQsFmNhYUF1dTXHjh1DqVQilUrJyMjg+vXreHh4MHbsWP785z8TEBDAypUr+fLLLykqKmqUryFUo+ksLCywt7cXamQDdBqR5XI5qampWtsN/aSnpaUxf/589u7dy1//+leWL19Ojx491O3rpKQkZDIZgwYNQiwWq0ekWVpa0rNnTyIiIti7dy9mZmZYW1vj4+PDK6+8wtatWykrKyMiIoI9e/bozV9X6vLyckpKSjA3N8fd3b1Rz6TAfTqFyBKJhCeffFIdStNEJY5cLuf27dusX7+ed955hxEjRhAdHc2wYcOws7NT15y5ublcuXKF0aNH4+Xlpb5wE4lEmJubY2trS79+/aisrOTw4cPq94nFYiQSCatXr+aLL77g119/5dVXXyUhIYGGhgaDnSL5+fncvn0bJycnXFxcsLKyeiSfmbHRKRpc1tbWeHp6kp+fT05ODj169NDaX1RUxOnTp9mzZw8uLi6sW7eOJ554QuvePKVSSXV1NWfOnMHc3JywsDB15EH15VC9fuKJJxg6dCiJiYmEh4fj7u6uFZkIDw+nf//+/Pjjj6xdu5ZnnnmGSZMmqbuyVZSWlnLt2jVcXFzUA/mFpoV+OkWNrCIrK4uMjAzgfk1cXFzMhQsXWLduHTt27ODll1/mX//6FwEBAeowmGYMODc3l4yMDKZPn65ur5qbm6svwFQhNisrK0aPHo2joyNnz56loaFBqw1uZmaGRCJh/vz5rF+/ntzcXD744AP279/PjRs31DVzUVER6enpuLm54e3trR5HLdCYTlEjq7hz5w5Xrlxh0KBB5OTkEBsbS3p6OqNHj+att97CyclJq+mhGqVmZmaGTCZj//79+Pv7M2DAAPU++L+OFZXQIpFI3fN39uxZ+vfvj7+/v94evMDAQDZs2MCxY8fYuXMnV65cYcCAAfTu3ZvMzEzy8/MZN24c3bt3bxQ6FPg/OpXIHh4e6skDZTIZPXr04O233yYgIEDvPBOa4qWkpJCfn8/cuXPVImp2rOgKKhKJGD58OJcuXeK3336jW7du2NjYNEqjymv8+PEMHDiQs2fPsnfvXvbt24dcLsfd3Z3u3bvj7e0tNCuaoFM1LQYMGICHhwd5eXk8++yzLFy4sNEdI5pCqpoWNTU1bNiwgSlTpuDn59eoh04lmG7vnbu7O1FRUZw5c4bMzMxGXw7d0JurqyuTJ09m2bJlKBQKLl++TL9+/fD398fFxeWRflbGRqcS2cnJidGjR+Pk5ISXl5c6lKU73kFX5h9++AF3d3f1HdGqQUC6ImtuV6Xr378/bm5u7N27l7q6ukbtbt2aWSQS4e/vT2FhIf7+/vj7+xMYGCh0hDRDpxIZYODAgfj5+TXqmIDGQpuZmZGVlcXWrVtZvXo1Dg4OWtEHzZFtgN4xFGKxmHnz5pGWlsbVq1f11sSqvFWsWrWK4uJiQkJC6NOnD126dGn/D8bI6XQii8ViZsyYQVZWFjExMVp3Oav+aj42bdrECy+8QM+ePfXWuKoHoFdyMzMz/Pz8mDVrFh9//LHe2l8z77i4OL799luGDRtGWFgYQUFBws2mLaDTiQzQo0cP1qxZwz//+U9SUlIa9aqp5Dpx4gTZ2dksWbJELaaqptYdZwzoFVyVZsaMGZSVlbF//36DYy0yMzOZO3cukZGR6kVzhAu8ltEpRQYYOnQoa9as4c033yQnJ0crWgFQU1PDrl27mDNnDmKxWOviT1No3WGXuuk0mxIffvghK1asoLKyUl0OVX63bt3iL3/5C08++STDhw9n6tSpQi9eK+i0IgNMnTqVGTNmMHv2bC5fvqyeyFAul7Nr1y6cnZ0ZPXo0FhYWetvP+sTWrLl1H4MHD2batGl8/PHH1NfXIxKJaGhoICsri2XLllFbW8tzzz3H888/L0jcSjq1yACLFy/mlVdeYf369ezbt089dcCZM2fUEQ59AutGN4BGAuuLGb/11lskJyeTkJBATU0Np06dYs2aNZiZmfHSSy8xceJE7O3tH+dHYpQIMR1g7ty5uLm58fPPP3P16lXKy8sJCgpi2LBh6tv4m7rg0jdyTV96kUiEo6MjL774Ip9//jlhYWHExsbi6urKyy+/zNChQwWJHxBBZO53ZEyYMAEXFxe+++47Lly4wMyZM5tcxFGzZ09zm+Zffe8RiUTY29uTkpJCcXExY8eOZdKkSfTq1UsYovkQCCL/f6ysrBg2bBhSqZTTp0+TkJDA2rVrmTRpknqkG9DotihNmhIY7o9z/v7778nMzCQyMpLIyEhCQkJwcXERQmwPiSCyBqopqjw9PQkPDyc+Pp7o6Gg+//xznnrqKUaNGtVoQXRDtbKK/Px8Tp06xbFjxygoKGDAgAGsWrUKLy8vXF1dhfBaGyGIrAexWEz37t3p2rUrEyZMIDU1lbi4OBYtWqSeHLxbt2507dqVrl274uXlhVKpJDMzk1u3bnHr1i3y8vJISEjg999/p0+fPowbN44RI0YgkUhwcHAQauA2RhC5CcRiMWKxmPHjxzNu3Djq6upISkoiLi6OU6dOcePGDW7cuEFBQQGVlZVMnjwZb29vpFIpvr6+zJ07l+HDhyORSARx2xlB5BYiEomwtrYmPDyc8PDwx10cAR06fRxZwDQQRBYwCQSRBUwCQWQBk0AQWcAkEEQWMAkEkQVMAkFkAZNAEFnAJBBEFjAJhC7qDkJdXR2pqancuXOn0Yg6TcrKyjhy5Ih6haoHYfDgwQaXIDZWBJE7ADKZjKNHj7Jr1y6tu7L1UVpayqFDh5pdXF13kFJ1dTUpKSlcu3aNXbt2MWPGjDYpe0dBEPkxI5PJiImJYf/+/YwfP56xY8dq3eyqiUgk4tKlS/z1r3/Fw8Oj0T5dVNtqa2s5evQolZWVJruQjiDyY0Qmk3H48GEOHjzIyJEjGTlypHpqLN3pCTS3qZ7r7tOVWbU+YGxsLDt37mTw4MFNNluMGeFi7zFRV1fH8ePH+eWXXxg+fDgjRoxALBY3u0Kqo6Ojuumhb/VUXU6ePMnGjRsZMmQI4eHhzTZJjBVB5MdAQ0MDp0+fZvv27eqaWCwWq/c3JXN0dLTWhV5TMp8+fZpVq1YRERFBeHi4Vh6mhiDyI0apVJKcnMyHH35IREQEY8eOVU/Gom8tatVz1euuXbtibm5uMK3q9enTp5kxYwbz5s0jLCxMa0kHU8Qk2sgKhYLa2tomL2SqqqqQyWTqtfYeBHNz84eaGVO1xO/KlSuZPXs248eP15pWQPVccyb8ptrB+tLK5XJOnTrFkiVLeO+99xg0aJBWelPF6EWWy+VcvXqVf/3rX5w8edJgzVNZWUlVVRVnz55tdR6VlZUUFBQQHBxMWlraA5f13LlzLFy4kKioKIKDgykoKAD0T+zS1KQvTU1DkJaWxoYNG1i4cCEDBw584LIaG0YtsmrB8Y0bN2JlZcXPP/+sDkvpChATE0NsbCwfffSR1jGam4uitLSU7du389133z10ef/whz/g4+NDVlYWGzdubLIczd2sqm+/6ubY6dOnM2TIEEB/NMMUMWqRr127RnR0NBYWFixYsAB3d3f1P073Z1f1tyVhK9X2kpIStm3bRmxsLH/605/YvHnzQ5W3sLCQ6OhoQP98zCp050zW/NvUtt9//53a2lr8/f21ZrhvD5nz8vIoLi4mICCgQ0zzZbQiX79+nTVr1uDo6Mj8+fPx9PRsJHFTkjYnc2FhIVu3buXSpUu89tpruLq6tkm5u3XrZlBU3e2G0uhuU2FmZqaeM6OlX1hNCgoK2LdvH8XFxept06dP1zvZ+PHjx8nOzmbx4sUdQmSjjFpkZGTwpz/9CVdXVxYuXKjVy6VZ+2r+1aWpsFVhYSGbN29Wr6nn5+fXZmVXKBRaUQjdXwvd1/rS6Euvj5bEmTXJz88nJiaGuro6vL298fb2xtbWVu8XoKCgAFtb2w4hMRhhjXzlyhWWLl1KSEgIc+fOxdnZGdB/Ba/518zMDCsrq2ajAsXFxWzZsoXr168zceJEdQ3aligUCq3JwTXLqcJQNEO3x6+1PYDN4eHhweTJk9VtbH3cvXuXGzduEBoair29Pd9++y1xcXHqtba3bdvG0aNHCQgIwNLSkjFjxjBmzJh2naTRqGpklcSDBw/m1VdfVS/wqK/21d0WGhrKkiVLDKaD+xd227ZtIy0tjYkTJ9K9e3etJXrbAtWx2qpm1ve6qXNsjtTUVGbOnEnfvn1ZunQpZWVljdKUlpZib2+Pt7c30dHR7NmzhxUrVlBbW8vnn39OfHw8H3/8MX379uXQoUMA7R7HNhqRr127xvLly+nXrx+zZ8/GwcGhyX+25nOlUomdnR3u7u6N9qmeV1ZWsmPHDuLj45k2bRrdu3fXmmCwM8g8dOhQTpw4QVJSErt37+b8+fNER0erFwxScfPmTWxtbXn//fe5fv06GzduJCgoiKqqKrZv387ixYsJDg5m0KBB+Pv7I5FImhzR1xYYTdNi8+bNxMbGEh8fz+eff661ry1++hUKBX5+frz55ptt2ibWRbfZ0x7NDH35GdqviYWFhbrDx8nJiRkzZhAXF6dVRoDc3Fx2795NYWGh1jXKuXPnsLOzY/z48cD9sdM9e/Z8JItdGo3IAB9++CGRkZF6Q1WtudrXF7NNT09n9erVWhK3R9hKn5BtLbO+mrk5mRUKBZWVlYhEIhwcHKirq6O8vFy9hrYKuVxOSUkJU6ZMwd3dnUOHDjFixAj8/PwoKipCqbw/4q66upqffvoJkUiEk5NTW3x0TWJUIkPji5vW/rNbe3HU1jLrK6+utBUVFaSnpyMSiTA3N8fHxwdvb+9mz083n9ach0wm48iRI1y5coWwsDBu3LhBYmIiK1eu1KqNi4uLycvLw8/Pj7lz53Ly5Em+//57Vq5cib+/P0qlkl9++YUbN25w5MgR5s6di62t7UN9Zi3BqERWKpWNai/VdhXtJXNbnoMmuiJmZ2ezd+9erl69ipOTExUVFQQHB/PKK69oxYj1nV9TNXFz52FjY0NgYKB6wUqAFStWMHz48EZfgEGDBtGrVy8cHR1ZvHgxp06dQqlUMnDgQJ5//nkOHDjAE088wZgxY+jVq9cjCdEZnchtLbPmMXTzag+Z9R1HVZ6SkhI++eQT7OzsWLNmDZ6enhQUFJCTk0NdXZ3BL6O+suq2xVtCcHAwn332WZNpPDw8mD17tvp1REQEERERACQmJhIVFUVISAgJCQl8//33SKXSFuX9sBiVyCoeRGbN92ru15Vatz3ZnjFkTUQiEYcPHyY/P59Nmzapu9t9fHzw8fFpUZtZXyRDM317I5fLWbZsGYGBgdTV1TF48GACAgLaPV8wQpE15WuNzPrSdDSZjx07xsCBA3F1dX2gC0BN9F3gtbfMQ4YMYdmyZQA4ODjQp08fdYdVe9MuIhcUFLB7925GjBihNR72YdGMoba1zPryamnYqrXnoBupgPuhqpKSEsaOHfvA0YyWRCva8lx0sbKyIioqqt2O3xQtjlLL5XK+/vprPDw88PDwYOrUqQbH5hYWFnLmzJl2CYLr/kNUMuv7WdXcZuinV9/xdPNq6/KrjqtZ7vr6epRKpboHTF8a3XLqO7+mzqE9JX7ctNi0+vp6oqOjuXPnDgkJCYjFYvbs2UNVVVWjtFVVVdTV1eHn54dCoVD/k+D+F6Kuro76+noaGhqQy+Ut/oD1yajarvkPVyqVbNiwgYCAAFJSUloss+Y23edtebGnT2YXFxeGDBnC3//+d/Xnc/HiRf72t79RWlraIplbcg7t0VTqCLS4aSEWi0lPTwfu3zcWEBBAbW0t9fX1Wulqa2tJS0vD2dkZa2trvvnmG3755Rc+/vhjvLy8+OCDD/jpp59wdHTE19cXqVTK//7v/zaap0Ef+v5pmj+dqp/i7OxsYmJi6NGjB6mpqQwYMECd1lAzQ/Ohr73ZVugrv2rbX/7yF27fvs2kSZMA6NmzJ6tXr0YikbSomaGbh+a5NDQ0kJ6ejlwu1+qqNxVa1UYuKiriypUr5Obmkpuby8yZMxtN3VRfX09lZSVSqZQtW7Zw5coV/v73vxMYGMhbb73FgQMHyMrKIi8vjzfeeAM7O7sWSQz6RQZtIe/du8eWLVuIjIzk3r17ZGZmqvep0jZ3Na/v4qgta+Sm2LBhg1ZvZXNtY31tZM0vpFJ5v6ftypUrpKSk8OKLLzJs2LA2OZeORItFVirvL4i4adMm6uvr6dGjB2KxmHv37uHg4KBOV11dTXJyMiUlJdjZ2bFu3Tr8/f3Vtwzt2bMHuB+ADwoKarHEKpoKXwHEx8dTVFTE0qVLOXv2LFu2bGn0D29KZn1p25IH+UIYqnn1dYjoSi2Xy7ly5QqpqalERUUxZcoUk5wWoMVtZJFIRGhoKN999x3ffvstUqmUr7/+mhs3bmilk8lkpKen4+HhgbOzs1qEjIwM6uvrCQ0NBaCkpIT8/PxGS+I2hb4LIM3H7du3OXnyJJMmTcLR0ZHevXtTUlJCVVVVk21Gfe1mzf1tib5yaz4MnZvme5u7ANTMKz09neTkZCIjI5k2bZrJTtDS4ho5MzOThIQEZs2ahbW1td4PRKlUkpubS5cuXVi9ejVffPEFMTExWjM/lpSUYGFhwYYNG8jNzRJAD9EAAAvDSURBVMXb27tVBVbVQLo1s2oOtcTEROrq6vjtt9+orKykoaGBrKwsQkJCGtXIhmo6zXzaWmRDvygq9J2b5j59568vDq5UKklLS+Ps2bPMmTOHyZMnm6zE0AqR7ezs2Llzp7ppYGFhQVRUFD4+Puo0SuX9yUcCAwMJDAwkPDycn376iaFDhxIUFET//v2ZPXs2zs7OuLm54ezsrPX+5tCscXT/mdnZ2eTl5fHiiy/i6+ur/iXIzs4mPz+fvn37tmqcgiq/tpa5JbV8W8h88eJFjh07xhtvvMGECRNMsjmhSYtF9vT0ZN26ddy7dw+ALl264Ovri52dnTqNmZkZL7zwAtOmTcPCwoLIyEgGDhyIl5cXEomEr776ipKSEuRyOcnJydjb22u9vzl0JVD9M6uqqoiNjcXGxoYpU6bg4uKiFjkuLo7//ve/PPvss+r3NFUz60Yt2lpmzehKUzyIzCpSUlLIyMjg3XffZdSoUeqZjEyZFossEokICgpqNp1mU0EikSCRSADYvXs3d+7cYfHixRQXF/Pll1/y3HPPtbrA+sJXtra2zJo1CzMzM+zt7bVEfeutt5qsvfQNttHdDjzUxCz6yt8eMquiNv/973/59NNPGTVqlNZdLqbMIxtrMW3aNKRSKUuWLMHe3p533nmHqVOntuoYTYXf7O3t9XYpa0ZUmvop1sxDd9RYUlIS69ev5+DBg60qr75yjho16qGO0Rxubm7s2LGjU0kMj3jQkG6Eo7U8aBShJe1KzeOq0tTX15OYmMi2bdvUcxg/DJrzRQi0LUY5+u1BaE5m3ePW1NSQmJjI0aNH+fbbbx9aYoH2xahEfti4blO9ZJp51NbWcuHCBVJTU1m7di1PPfXUQ5VboP0xOpFVtemDRhKaG59QU1PD+fPnyczMZOnSpYwdO7ZTtTWNFaMTWbN360EnTzEkc01NDefOnSMnJ4dXX32VcePGtevsOAJth1GJDNq1skKheOCxEPp6w/Ly8rh27Rrz589n/PjxJt0TZmoYlcjbtm1T9yyC/gE9mtua26+5rbq6GqlUyqJFi3j66acFiY0MkbKtBxO0E3fv3qW8vPyB33/s2DHi4+NZs2aNwTTW1ta4urp2ip4wU8NoamRnZ+eHupHRw8ODLl260L179zYslUBHwWgmMRQQaApBZAGTQBBZwCQQRBYwCQSRBUwCQWQBk0AQWcAkEEQWMAkEkQVMAkFkAZNAEFnAJBBEFjAJBJEFTAJBZAGTQBBZwCQQRBYwCQSRBUwCQWQBk8BobnVqCqVSiUwma7SeiSY1NTXU1dWpZxN9EMzMzFo1e6jAo8Nobj41hEKh4OrVq6xbt47jx4+rl/fSvVu6qqqKqqqqB1oIprq6mt9//53g4OA2m5VToG0x6hpZJfGnn36KhYUF+/btw9PTE2g8LUBMTAyxsbF89NFHWscwNC+GantZWRk7duxg+/bt7XQWAm2BUbeRr1+/TnR0NHK5nEWLFuHh4aF3ds2m1gRpaumFkpIStmzZwsGDB1m6dGk7nYVAW2C0NXJmZiZr167Fzs6ORYsW4enp2WhuY93Z51UYmpVek6KiIrZt20ZKSgrz58/Hzc2t3c9J4MExyhr56tWrLFu2jC5duqhrYhX6VjoCsLW11ZKxqZq5qKiILVu2kJ6ezvTp0+nWrVu7nYtA22B0NXJGRgbLly8nMDCQefPm4eLiAjReQFy3Zu7bty9+fn5606lQNSe2bt1KRkYGzz77LN27dzfJJW9NDaMSOSMjg2XLltG/f39eeuklJBKJ3oVtoLHMEolEvUqrIZnLysr45ptvuHTpElOmTKFHjx4PPOOnwKPFaJoW165dY8WKFQQHBzN79my6dOmi9yLO0EWeoX2q55WVlezYsYOTJ08ydepUevbsqTUvsiBzx8ZoauTNmzdz5MgRjh07xsaNG9v8+Eqlkh49evDmm2/i5+fX5scXaF+MRmSAjz76iMjIyEYxYtUD0FrKS7VNc7/mc8106enprF69WktiQ1EPgY6H0TQtVOhbb1lzm0Kh0Nqn+57mYsktjTMLdCyMSmTVbPWCzAK6GJ3I7Smzbl5NvRboWBiVyCpaI7M+IXVlbiqaIWActJvImZmZ7Ny5k+zs7DY9rqaELZHZkKytCc0JdHxaLXJlZSWbNm3iueee49SpUwbTZWZmEh8fj0wme6gCaqJPvraUWV9ehvYLdCxaFX67c+cOy5Ytw9bWFmdnZ8rKygymVe1TDatsK/R1P+suyatKp8LQSqe6vYKax9d9LtCxaVWN7OHhwffff8+KFSsQi8UG01VUVHDlyhWcnJxwdHRk06ZNDB48mMLCQhQKBatWrcLc3Bx/f3+effZZ3nnnnRYtOK6vZlVtVygUKBQK5HK5+rlubW2oGdGSiz6hVu7YtEsbuaamBktLS6RSKdHR0cTFxfGf//wHd3d33n77bQ4dOoRcLueHH36gpqYGFxcXXF1dmz2upsj6mgoxMTFMmTKFkSNHMnr0aEJCQrh+/breaIahpkhzoTmBjkm7iFxaWkpOTg4//vgjiYmJ/OMf/6BHjx5UVlbyz3/+k88++wwAJycn+vXr1+KxvvqE05QsNzeXMWPGsG/fPuLi4njqqafUC0w2J7O+fHS3CXRc2kXk8vJyLl68iLm5OV27dlWvIpqSkoJIJGL48OEA3L59m4aGhlatfafZXNB8yGQyysvL8fDwwNbWlrKyMmpra/H19dUbOzYkc0vjzAIdizYfayGXy7l58yY9evTg9ddfZ9u2bZw9e5aJEydSV1cHwL1796ipqWH79u3cuXOnxReEmhJqjqkAuHXrFoWFhVRUVFBTU8Pt27dRKpU888wz6vfqXsRpLsyu29TQvAAULvg6Pq0SuaKigm+++YbU1FRSU1O5efMmmZmZzJkzR93GrampISMjg27duhEWFkZCQgK7d+9m4MCBBAcH4+/vz4oVK5BIJNy5cwc3N7dW3UakK6GKu3fvYmlpiUQiQaFQIBaLEYlEVFZWIpFIGompeZymbocSamXjoFUiW1paEhQUhKenp7qmc3Jy0opgWFtbExkZiYWFBdbW1syaNYtr166pB7Z/9dVX3L59GzMzMxwdHRGLxdjb27cof82aU1fmwsJC7O3teeGFF/D19aWmpobQ0FAyMzPx8vJSv0efzIaaEYLMxkOrRLaxsWHcuHFNprG0tKRv377q1z4+Pvj4+ACwZ88eamtrmTVrFtevX+f48eNMnjy5xfnrCqeSub6+nry8PCwsLNQD7g8ePIiLiwvBwcGN4syGZFbloe/GVEHmjs0jHY88btw4/Pz8WL16NY6Ojrz22muMHj26VcfQFUokElFTU8Pdu3f5+eefiYmJwczMDBsbG3bs2IFEIgFoUmbNYxtqF1++fLl1JyvwSHmkIjs4OFBUVKR+bWZm1qoLKUNNgC5duvDGG2+wfPly9cB5MzMz9a1K+trVhmpZ3Z5DgOTkZNavX8++fftadb4Cj45HfoeI5n1wraWpkJhKXs07Rgxd3OmTWfO4qjT19fUkJyfz9ddfs3//fkaNGvXAZRdoX4zqVid48I6J5mTWPW5tbS2JiYnExMSwc+dOQeIOjlGJ/LCdFPou7lTbNfOQyWRcuHCB5ORkPvjgg1a34wUePUYnsqo2fdBIQlNtY7gfB79w4QLXrl1j6dKlPP300w/VHBJ4NBidyKqHZq9cazEkc01NDefPnyc7O5t58+YRERGBtbV1WxRdoJ0xKpFBu1Y21CvXEnRlViqV5Ofnc/XqVf7whz/wzDPPqMeICHR8jErkf//73+zdu1f9Wt/8FK15rbmturoab29vFixYwPjx4wWJjQyjmbG+uLi4yTtS2gKxWIy7uztWVlbtmo9A22M0IgsINIVRTgcgIKCLILKASSCILGASCCILmASCyAImgSCygEkgiCxgEggiC5gEgsgCJoEgsoBJIIgsYBIIIguYBILIAiaBILKASSCILGASCCILmASCyAImgSCygEkgiCxgEggiC5gE/w9/sMsqQhjmZQAAAABJRU5ErkJggg==)
Three weight A, B and C are connected by string as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting A and B is (where g is acceleration due to gravity)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALIAAADTCAYAAAAlIkmXAAAgAElEQVR4nO2deVhTV974P2ENm2EHIYBLBUTEtSrgUrVKrYhWba2+2lo7daszaq0z1b7Tdqyd6bSO0trNunS09qmdVlu3iiuIO5tYHERlx7qwyCJbgCS/P/wlbxISFgUl4X6eJw/JvSf3nBs+OTn3e849R6RUKpUICBg5Zo+7AAICbYEgsoBJIIgsYBIIIguYBILIAiaBILKASSCILGASWDzuAjwMDQ0Nj7sIHRJzc3NEItHjLsYjxahFrqure9xF6JCIxWJBZGOitrb2cRehQ2JlZYWZWedqNRq1yNXV1Y+7CB0Se3v7x12ER45Ri1xRUfG4i9AhcXFxedxFeOQYtchlZWWPuwgdErlc/riL8MgRRDZBOmM0x6hFLi4uftxF6JB0RpFFwnjkB+P27dvU1tbi6uqKjY0NDQ0NlJaWUl5eTkBAwOMuXqejc8VoBEwWQWQBk0AQWcAkEEQWMAkEkQVMAkFkAZNAEFnAJBBEFjAJBJEFTAJBZAGTQBBZwCQQRBYwCQSRBUwCQWQBk0AQWcAkMOqB9Y+a+vp6MjIySE5OxsnJiX79+jVKc+vWLT755BPs7e3p3r07ffr0wdfXF29vbywtLR9DqTsHgsgtIC0tjUOHDnHs2DFqa2sZPHgwYWFhetOKxWJ69+5NQUEBu3fvZtOmTfj4+NCrVy9GjBhBYGAgvXv3fsRnYPoId4gYoLq6mvj4eP7xj39QXFxMVFQUU6dOZdCgQYhEIu7cuaP3DpGysjL1HSJKpZLr16+zb98+du3aRXFxMUOGDOHJJ59k5MiRhISEYGtr+5jP1DQQRNZAqVRSU1PD5cuXef/998nKyuLdd99l+vTpmJubq9MALRIZ0Jrx5/Tp0yxYsID6+npCQ0Pp168fY8eOJTAwECsrq043O1BbIjQt/j9yuZzc3Fx+/PFHkpKSCAkJobKykp49eyISiXjQ77vm+wICAnBzc2PMmDEkJiby66+/kpWVxciRIwkPD6dr167qL4xA6xBEBhQKBRcvXmTnzp1UVFSwYsUKQkND+eSTT/juu+8IDg7G2tpaS8qmxNa3T6FQsH79egYPHsw777xDfn4+69evJy0tjYqKCkpKShg5ciS9e/cWZH4AhPAbcOLECbZu3Yq7uztr164lNDQUpVLJ3LlzycnJIT4+Xi2nUqlstnZWpdFMl5ycTGJiIq+//jpKpRJfX1/ee+89Zs+eTXl5OfHx8ezbt49Lly51yglWHpZOXyP/+uuvfPbZZ7zyyitERETg4OCgFtDBwYFFixbxt7/9jUGDBiGRSIDmZVYoFADqJklZWRkbN27k5Zdfxs/PT30MiUTCjBkz8PHx4ZNPPiEpKQkzMzMqKysJCwvDwqLT/3taTKeukU+fPs1XX33F/PnzmTp1Kg4ODoC2qE899RS9e/dmy5YtKJVKFApFsyKr9qvSHjp0CGtrayIiIhrV1jY2NowZM4Y///nP1NXV8dtvv3H27FnOnz/f/h+ACdFpRU5PT+f999/nf/7nf4iKilJPw6rbDjY3N+edd97hp59+IiUlBYVCoa5x9aESWPW4fv06R48eZc6cOTg6OmpJrPorEokIDw9n+fLlpKamkpWVRUJCAhcvXmzHT8C06JQi5+fn8+677zJu3DiioqLUYS/ddrCqRvX09GTOnDmsW7dOa7shVBIrlUoOHDhAt27dCAwMVDc1dB9wX+aRI0fy9ttvc/DgQW7cuEFycjKFhYXt/4GYAJ1S5I0bN5KUlMSQIUOwtrYGDEuskvLFF1/E0tKSEydONFkrK5VK5HI5crmchIQEMjMzGTduHBKJRKtZok9mCwsLIiIisLGx4fjx49y6dYvExMRH86EYOZ1O5MuXL1NcXMzLL7/M/Pnz+eMf/0hJSYnWMg6aMqvks7GxYc6cOXz22WfcvHmz2Rq5srKSQ4cOIZVK6dWrV6Pjab6/oaGBiooKtm3bRnh4ODNnzkQsFpOTk0NmZiZpaWkPHMfuLHQqkWUyGSdOnKB379788Y9/JCkpCQ8PDyZPnsy///1v8vLykMlkjS7qVLVvr1696N69O/v27Wtyxsv6+nrOnz/PvXv3GDNmDHZ2do2Op1QqaWhooLi4mCNHjrB06VISExPZtWsXa9asYcmSJWRnZ1NYWEhmZiZVVVWP6mMySszfe++99x53IR4VFy9eJD4+ngkTJuDv74+VlRUjR44kNDSUvXv3Ehsbi7m5Ofb29ojFYgAt8cRiMba2tpw7dw5PT09cXFywtbXF0tIShUJBbW0t1dXVVFVVsXfvXqRSKePGjdN7IVlZWcmFCxf48ccfuXjxIuPHj+f111/H19cXkUhE165dOXPmDKWlpTg4OODm5oarq6vQjW2ATiOyTCbj8OHDKJVKJk6cqBYVwM3NjZEjR6JQKEhKSiI1NZV79+7h6empllQloZ2dHbm5ueTn59O/f/9GIldUVJCamkp2djbTp0/HyclJqxxKpZJLly5x4MABzp49i6enJwsWLCA0NFRrvIWVlRVKpZITJ07g4uKCk5OTMBS0CTpNxL2oqIhbt27Rp08frY4NuN+mtbOzY9q0aYSGhvLLL78QFxfHtWvXGDJkCAMHDkQkEqFQKLC3t2fw4MHcvHlTbz53797lxIkThIeHI5VKtTpHCgoKiI2N5erVq7i5ufHSSy/Rt2/fRt3fIpEIS0tLgoODcXFxobS0lPz8fMrKyrCxsWnnT8o46TQi37x5k/LycgIDA7W268aNPTw8mDNnDpmZmVy8eJEtW7bg4+PDggUL6NKlCwqFgoCAALy8vPTmU19fj4WFBWFhYcjlcpRKJeXl5cTFxREbG4tUKiUqKoqQkBCcnZ3VITnNJoPqtZubG0FBQVy/fp3CwkLKysrw9PQUmhd66BQi19fXk5OTg7m5OT179gQaC6z5sLa2pnfv3vj6+uLv78/+/fuZN28es2fPJjIyEktLS4M1o6OjI5MmTcLBwQG5XE5ycjLbtm3DxcWFGTNmEBAQQNeuXTEzM1MLq8pXV1AnJycCAwM5f/48VVVV3Lp1i+7du2s1iwTu0ylELi8vJzs7m8DAQHXcWEVTQovFYkJCQpBKpURGRrJ161b+85//8PrrrxMUFKQ3LxsbGwIDA8nPz2fXrl3k5+fz9NNPM2LECKRSKebm5igUCr0C68psYWFBt27dkEgklJeXU1ZWRn19vSCyHjqFyDKZjMrKSgYNGqS1valhmZpCd+nShcDAQFavXk1cXBybN28mLCyMl156qVFetbW1HDlyhP379xMcHMzKlSvx8/PD0tLSYEeIKj99zQxnZ2fc3Nyoq6ujtLSU+vr6tvpYTIpOIXJdXR1VVVU4Ozs3mU5XMN14sr29PRMmTCAkJIR79+6p09TU1KgfhYWF7N27l8WLFzNkyBD1Auf65NXM01C719bWFjs7O0pLSwWRm6BTdIjU19dTVVWFo6MjYLj2NbRNtxZ1d3fH19cXgOzsbObPn4+XlxcLFy5EJpPx6aef0r9//0Zd0i3NT7OMtra22NraUl9fT11dXZMDljoznaZGLi4uJjc3l6ysLL2C6o6tUD1XRR4aGhrU++RyOV5eXgQFBbFlyxYOHDhAQ0MDx48fRy6Xq+/xUz3MzMzUf/U9RCIRIpFI6zncD8NVV1eTl5dHTU0NSqWSGzdu4O7uLtxFokOnEFkul1NcXMylS5dIT09Xb9cVWvO5IcnlcjlFRUWMGDGCoKAgiouLkclkwP149G+//UZycjJ+fn74+flhbW3dSFZA/Ve1XVdgFQqFgoyMDDw8PGhoaGD9+vV88cUXjTpaOjudQmQzMzOkUimvvfaa1h0g+mpiuVyu9VdVEzc0NFBZWcnp06dJSkpCKpUC8MILL1BQUMC5c+fw9/dn6tSpVFdXU15ejlQqJSIiAqlUioWFhVYtbaiG1pRdJBJRU1PD+vXruXjxIubm5pw6dUr9xRH4PzqFyFZWVuoLJtVdICp075A2VDumpaVx5MgRysvLeeKJJ+jVqxcAI0eOxNXVlfT0dJydnfH29qaiooLff/+dlJQUNm3aRFhYGE8//TT29vaNLuo089LMT0V1dTUymQyxWIyNjY3QpDBAp7jYs7S0VIsMjWXRFzFQCXbnzh2++uorvvzyS1xcXJg5cyZRUVHk5OTwww8/kJubi5eXF4cPHyYoKIiUlBQOHjxIWFgYs2fPZvjw4Rw9epR3332XGzduaB1bV2B9QqtEtra2xt7eXriPzwCdQmQrKytkMhnJyckG0+jK1dDQwP79+5k/fz7l5eWsWrWK559/Hn9/f0pKSkhMTEQsFmNhYUF1dTXHjh1DqVQilUrJyMjg+vXreHh4MHbsWP785z8TEBDAypUr+fLLLykqKmqUryFUo+ksLCywt7cXamQDdBqR5XI5qampWtsN/aSnpaUxf/589u7dy1//+leWL19Ojx491O3rpKQkZDIZgwYNQiwWq0ekWVpa0rNnTyIiIti7dy9mZmZYW1vj4+PDK6+8wtatWykrKyMiIoI9e/bozV9X6vLyckpKSjA3N8fd3b1Rz6TAfTqFyBKJhCeffFIdStNEJY5cLuf27dusX7+ed955hxEjRhAdHc2wYcOws7NT15y5ublcuXKF0aNH4+Xlpb5wE4lEmJubY2trS79+/aisrOTw4cPq94nFYiQSCatXr+aLL77g119/5dVXXyUhIYGGhgaDnSL5+fncvn0bJycnXFxcsLKyeiSfmbHRKRpc1tbWeHp6kp+fT05ODj169NDaX1RUxOnTp9mzZw8uLi6sW7eOJ554QuvePKVSSXV1NWfOnMHc3JywsDB15EH15VC9fuKJJxg6dCiJiYmEh4fj7u6uFZkIDw+nf//+/Pjjj6xdu5ZnnnmGSZMmqbuyVZSWlnLt2jVcXFzUA/mFpoV+OkWNrCIrK4uMjAzgfk1cXFzMhQsXWLduHTt27ODll1/mX//6FwEBAeowmGYMODc3l4yMDKZPn65ur5qbm6svwFQhNisrK0aPHo2joyNnz56loaFBqw1uZmaGRCJh/vz5rF+/ntzcXD744AP279/PjRs31DVzUVER6enpuLm54e3trR5HLdCYTlEjq7hz5w5Xrlxh0KBB5OTkEBsbS3p6OqNHj+att97CyclJq+mhGqVmZmaGTCZj//79+Pv7M2DAAPU++L+OFZXQIpFI3fN39uxZ+vfvj7+/v94evMDAQDZs2MCxY8fYuXMnV65cYcCAAfTu3ZvMzEzy8/MZN24c3bt3bxQ6FPg/OpXIHh4e6skDZTIZPXr04O233yYgIEDvPBOa4qWkpJCfn8/cuXPVImp2rOgKKhKJGD58OJcuXeK3336jW7du2NjYNEqjymv8+PEMHDiQs2fPsnfvXvbt24dcLsfd3Z3u3bvj7e0tNCuaoFM1LQYMGICHhwd5eXk8++yzLFy4sNEdI5pCqpoWNTU1bNiwgSlTpuDn59eoh04lmG7vnbu7O1FRUZw5c4bMzMxGXw7d0JurqyuTJ09m2bJlKBQKLl++TL9+/fD398fFxeWRflbGRqcS2cnJidGjR+Pk5ISXl5c6lKU73kFX5h9++AF3d3f1HdGqQUC6ImtuV6Xr378/bm5u7N27l7q6ukbtbt2aWSQS4e/vT2FhIf7+/vj7+xMYGCh0hDRDpxIZYODAgfj5+TXqmIDGQpuZmZGVlcXWrVtZvXo1Dg4OWtEHzZFtgN4xFGKxmHnz5pGWlsbVq1f11sSqvFWsWrWK4uJiQkJC6NOnD126dGn/D8bI6XQii8ViZsyYQVZWFjExMVp3Oav+aj42bdrECy+8QM+ePfXWuKoHoFdyMzMz/Pz8mDVrFh9//LHe2l8z77i4OL799luGDRtGWFgYQUFBws2mLaDTiQzQo0cP1qxZwz//+U9SUlIa9aqp5Dpx4gTZ2dksWbJELaaqptYdZwzoFVyVZsaMGZSVlbF//36DYy0yMzOZO3cukZGR6kVzhAu8ltEpRQYYOnQoa9as4c033yQnJ0crWgFQU1PDrl27mDNnDmKxWOviT1No3WGXuuk0mxIffvghK1asoLKyUl0OVX63bt3iL3/5C08++STDhw9n6tSpQi9eK+i0IgNMnTqVGTNmMHv2bC5fvqyeyFAul7Nr1y6cnZ0ZPXo0FhYWetvP+sTWrLl1H4MHD2batGl8/PHH1NfXIxKJaGhoICsri2XLllFbW8tzzz3H888/L0jcSjq1yACLFy/mlVdeYf369ezbt089dcCZM2fUEQ59AutGN4BGAuuLGb/11lskJyeTkJBATU0Np06dYs2aNZiZmfHSSy8xceJE7O3tH+dHYpQIMR1g7ty5uLm58fPPP3P16lXKy8sJCgpi2LBh6tv4m7rg0jdyTV96kUiEo6MjL774Ip9//jlhYWHExsbi6urKyy+/zNChQwWJHxBBZO53ZEyYMAEXFxe+++47Lly4wMyZM5tcxFGzZ09zm+Zffe8RiUTY29uTkpJCcXExY8eOZdKkSfTq1UsYovkQCCL/f6ysrBg2bBhSqZTTp0+TkJDA2rVrmTRpknqkG9DotihNmhIY7o9z/v7778nMzCQyMpLIyEhCQkJwcXERQmwPiSCyBqopqjw9PQkPDyc+Pp7o6Gg+//xznnrqKUaNGtVoQXRDtbKK/Px8Tp06xbFjxygoKGDAgAGsWrUKLy8vXF1dhfBaGyGIrAexWEz37t3p2rUrEyZMIDU1lbi4OBYtWqSeHLxbt2507dqVrl274uXlhVKpJDMzk1u3bnHr1i3y8vJISEjg999/p0+fPowbN44RI0YgkUhwcHAQauA2RhC5CcRiMWKxmPHjxzNu3Djq6upISkoiLi6OU6dOcePGDW7cuEFBQQGVlZVMnjwZb29vpFIpvr6+zJ07l+HDhyORSARx2xlB5BYiEomwtrYmPDyc8PDwx10cAR06fRxZwDQQRBYwCQSRBUwCQWQBk0AQWcAkEEQWMAkEkQVMAkFkAZNAEFnAJBBEFjAJhC7qDkJdXR2pqancuXOn0Yg6TcrKyjhy5Ih6haoHYfDgwQaXIDZWBJE7ADKZjKNHj7Jr1y6tu7L1UVpayqFDh5pdXF13kFJ1dTUpKSlcu3aNXbt2MWPGjDYpe0dBEPkxI5PJiImJYf/+/YwfP56xY8dq3eyqiUgk4tKlS/z1r3/Fw8Oj0T5dVNtqa2s5evQolZWVJruQjiDyY0Qmk3H48GEOHjzIyJEjGTlypHpqLN3pCTS3qZ7r7tOVWbU+YGxsLDt37mTw4MFNNluMGeFi7zFRV1fH8ePH+eWXXxg+fDgjRoxALBY3u0Kqo6Ojuumhb/VUXU6ePMnGjRsZMmQI4eHhzTZJjBVB5MdAQ0MDp0+fZvv27eqaWCwWq/c3JXN0dLTWhV5TMp8+fZpVq1YRERFBeHi4Vh6mhiDyI0apVJKcnMyHH35IREQEY8eOVU/Gom8tatVz1euuXbtibm5uMK3q9enTp5kxYwbz5s0jLCxMa0kHU8Qk2sgKhYLa2tomL2SqqqqQyWTqtfYeBHNz84eaGVO1xO/KlSuZPXs248eP15pWQPVccyb8ptrB+tLK5XJOnTrFkiVLeO+99xg0aJBWelPF6EWWy+VcvXqVf/3rX5w8edJgzVNZWUlVVRVnz55tdR6VlZUUFBQQHBxMWlraA5f13LlzLFy4kKioKIKDgykoKAD0T+zS1KQvTU1DkJaWxoYNG1i4cCEDBw584LIaG0YtsmrB8Y0bN2JlZcXPP/+sDkvpChATE0NsbCwfffSR1jGam4uitLSU7du389133z10ef/whz/g4+NDVlYWGzdubLIczd2sqm+/6ubY6dOnM2TIEEB/NMMUMWqRr127RnR0NBYWFixYsAB3d3f1P073Z1f1tyVhK9X2kpIStm3bRmxsLH/605/YvHnzQ5W3sLCQ6OhoQP98zCp050zW/NvUtt9//53a2lr8/f21ZrhvD5nz8vIoLi4mICCgQ0zzZbQiX79+nTVr1uDo6Mj8+fPx9PRsJHFTkjYnc2FhIVu3buXSpUu89tpruLq6tkm5u3XrZlBU3e2G0uhuU2FmZqaeM6OlX1hNCgoK2LdvH8XFxept06dP1zvZ+PHjx8nOzmbx4sUdQmSjjFpkZGTwpz/9CVdXVxYuXKjVy6VZ+2r+1aWpsFVhYSGbN29Wr6nn5+fXZmVXKBRaUQjdXwvd1/rS6Euvj5bEmTXJz88nJiaGuro6vL298fb2xtbWVu8XoKCgAFtb2w4hMRhhjXzlyhWWLl1KSEgIc+fOxdnZGdB/Ba/518zMDCsrq2ajAsXFxWzZsoXr168zceJEdQ3aligUCq3JwTXLqcJQNEO3x6+1PYDN4eHhweTJk9VtbH3cvXuXGzduEBoair29Pd9++y1xcXHqtba3bdvG0aNHCQgIwNLSkjFjxjBmzJh2naTRqGpklcSDBw/m1VdfVS/wqK/21d0WGhrKkiVLDKaD+xd227ZtIy0tjYkTJ9K9e3etJXrbAtWx2qpm1ve6qXNsjtTUVGbOnEnfvn1ZunQpZWVljdKUlpZib2+Pt7c30dHR7NmzhxUrVlBbW8vnn39OfHw8H3/8MX379uXQoUMA7R7HNhqRr127xvLly+nXrx+zZ8/GwcGhyX+25nOlUomdnR3u7u6N9qmeV1ZWsmPHDuLj45k2bRrdu3fXmmCwM8g8dOhQTpw4QVJSErt37+b8+fNER0erFwxScfPmTWxtbXn//fe5fv06GzduJCgoiKqqKrZv387ixYsJDg5m0KBB+Pv7I5FImhzR1xYYTdNi8+bNxMbGEh8fz+eff661ry1++hUKBX5+frz55ptt2ibWRbfZ0x7NDH35GdqviYWFhbrDx8nJiRkzZhAXF6dVRoDc3Fx2795NYWGh1jXKuXPnsLOzY/z48cD9sdM9e/Z8JItdGo3IAB9++CGRkZF6Q1WtudrXF7NNT09n9erVWhK3R9hKn5BtLbO+mrk5mRUKBZWVlYhEIhwcHKirq6O8vFy9hrYKuVxOSUkJU6ZMwd3dnUOHDjFixAj8/PwoKipCqbw/4q66upqffvoJkUiEk5NTW3x0TWJUIkPji5vW/rNbe3HU1jLrK6+utBUVFaSnpyMSiTA3N8fHxwdvb+9mz083n9ach0wm48iRI1y5coWwsDBu3LhBYmIiK1eu1KqNi4uLycvLw8/Pj7lz53Ly5Em+//57Vq5cib+/P0qlkl9++YUbN25w5MgR5s6di62t7UN9Zi3BqERWKpWNai/VdhXtJXNbnoMmuiJmZ2ezd+9erl69ipOTExUVFQQHB/PKK69oxYj1nV9TNXFz52FjY0NgYKB6wUqAFStWMHz48EZfgEGDBtGrVy8cHR1ZvHgxp06dQqlUMnDgQJ5//nkOHDjAE088wZgxY+jVq9cjCdEZnchtLbPmMXTzag+Z9R1HVZ6SkhI++eQT7OzsWLNmDZ6enhQUFJCTk0NdXZ3BL6O+suq2xVtCcHAwn332WZNpPDw8mD17tvp1REQEERERACQmJhIVFUVISAgJCQl8//33SKXSFuX9sBiVyCoeRGbN92ru15Vatz3ZnjFkTUQiEYcPHyY/P59Nmzapu9t9fHzw8fFpUZtZXyRDM317I5fLWbZsGYGBgdTV1TF48GACAgLaPV8wQpE15WuNzPrSdDSZjx07xsCBA3F1dX2gC0BN9F3gtbfMQ4YMYdmyZQA4ODjQp08fdYdVe9MuIhcUFLB7925GjBihNR72YdGMoba1zPryamnYqrXnoBupgPuhqpKSEsaOHfvA0YyWRCva8lx0sbKyIioqqt2O3xQtjlLL5XK+/vprPDw88PDwYOrUqQbH5hYWFnLmzJl2CYLr/kNUMuv7WdXcZuinV9/xdPNq6/KrjqtZ7vr6epRKpboHTF8a3XLqO7+mzqE9JX7ctNi0+vp6oqOjuXPnDgkJCYjFYvbs2UNVVVWjtFVVVdTV1eHn54dCoVD/k+D+F6Kuro76+noaGhqQy+Ut/oD1yajarvkPVyqVbNiwgYCAAFJSUloss+Y23edtebGnT2YXFxeGDBnC3//+d/Xnc/HiRf72t79RWlraIplbcg7t0VTqCLS4aSEWi0lPTwfu3zcWEBBAbW0t9fX1Wulqa2tJS0vD2dkZa2trvvnmG3755Rc+/vhjvLy8+OCDD/jpp59wdHTE19cXqVTK//7v/zaap0Ef+v5pmj+dqp/i7OxsYmJi6NGjB6mpqQwYMECd1lAzQ/Ohr73ZVugrv2rbX/7yF27fvs2kSZMA6NmzJ6tXr0YikbSomaGbh+a5NDQ0kJ6ejlwu1+qqNxVa1UYuKiriypUr5Obmkpuby8yZMxtN3VRfX09lZSVSqZQtW7Zw5coV/v73vxMYGMhbb73FgQMHyMrKIi8vjzfeeAM7O7sWSQz6RQZtIe/du8eWLVuIjIzk3r17ZGZmqvep0jZ3Na/v4qgta+Sm2LBhg1ZvZXNtY31tZM0vpFJ5v6ftypUrpKSk8OKLLzJs2LA2OZeORItFVirvL4i4adMm6uvr6dGjB2KxmHv37uHg4KBOV11dTXJyMiUlJdjZ2bFu3Tr8/f3Vtwzt2bMHuB+ADwoKarHEKpoKXwHEx8dTVFTE0qVLOXv2LFu2bGn0D29KZn1p25IH+UIYqnn1dYjoSi2Xy7ly5QqpqalERUUxZcoUk5wWoMVtZJFIRGhoKN999x3ffvstUqmUr7/+mhs3bmilk8lkpKen4+HhgbOzs1qEjIwM6uvrCQ0NBaCkpIT8/PxGS+I2hb4LIM3H7du3OXnyJJMmTcLR0ZHevXtTUlJCVVVVk21Gfe1mzf1tib5yaz4MnZvme5u7ANTMKz09neTkZCIjI5k2bZrJTtDS4ho5MzOThIQEZs2ahbW1td4PRKlUkpubS5cuXVi9ejVffPEFMTExWjM/lpSUYGFhwYYNG8jNzRJAD9EAAAvDSURBVMXb27tVBVbVQLo1s2oOtcTEROrq6vjtt9+orKykoaGBrKwsQkJCGtXIhmo6zXzaWmRDvygq9J2b5j59568vDq5UKklLS+Ps2bPMmTOHyZMnm6zE0AqR7ezs2Llzp7ppYGFhQVRUFD4+Puo0SuX9yUcCAwMJDAwkPDycn376iaFDhxIUFET//v2ZPXs2zs7OuLm54ezsrPX+5tCscXT/mdnZ2eTl5fHiiy/i6+ur/iXIzs4mPz+fvn37tmqcgiq/tpa5JbV8W8h88eJFjh07xhtvvMGECRNMsjmhSYtF9vT0ZN26ddy7dw+ALl264Ovri52dnTqNmZkZL7zwAtOmTcPCwoLIyEgGDhyIl5cXEomEr776ipKSEuRyOcnJydjb22u9vzl0JVD9M6uqqoiNjcXGxoYpU6bg4uKiFjkuLo7//ve/PPvss+r3NFUz60Yt2lpmzehKUzyIzCpSUlLIyMjg3XffZdSoUeqZjEyZFossEokICgpqNp1mU0EikSCRSADYvXs3d+7cYfHixRQXF/Pll1/y3HPPtbrA+sJXtra2zJo1CzMzM+zt7bVEfeutt5qsvfQNttHdDjzUxCz6yt8eMquiNv/973/59NNPGTVqlNZdLqbMIxtrMW3aNKRSKUuWLMHe3p533nmHqVOntuoYTYXf7O3t9XYpa0ZUmvop1sxDd9RYUlIS69ev5+DBg60qr75yjho16qGO0Rxubm7s2LGjU0kMj3jQkG6Eo7U8aBShJe1KzeOq0tTX15OYmMi2bdvUcxg/DJrzRQi0LUY5+u1BaE5m3ePW1NSQmJjI0aNH+fbbbx9aYoH2xahEfti4blO9ZJp51NbWcuHCBVJTU1m7di1PPfXUQ5VboP0xOpFVtemDRhKaG59QU1PD+fPnyczMZOnSpYwdO7ZTtTWNFaMTWbN360EnTzEkc01NDefOnSMnJ4dXX32VcePGtevsOAJth1GJDNq1skKheOCxEPp6w/Ly8rh27Rrz589n/PjxJt0TZmoYlcjbtm1T9yyC/gE9mtua26+5rbq6GqlUyqJFi3j66acFiY0MkbKtBxO0E3fv3qW8vPyB33/s2DHi4+NZs2aNwTTW1ta4urp2ip4wU8NoamRnZ+eHupHRw8ODLl260L179zYslUBHwWgmMRQQaApBZAGTQBBZwCQQRBYwCQSRBUwCQWQBk0AQWcAkEEQWMAkEkQVMAkFkAZNAEFnAJBBEFjAJBJEFTAJBZAGTQBBZwCQQRBYwCQSRBUwCQWQBk8BobnVqCqVSiUwma7SeiSY1NTXU1dWpZxN9EMzMzFo1e6jAo8Nobj41hEKh4OrVq6xbt47jx4+rl/fSvVu6qqqKqqqqB1oIprq6mt9//53g4OA2m5VToG0x6hpZJfGnn36KhYUF+/btw9PTE2g8LUBMTAyxsbF89NFHWscwNC+GantZWRk7duxg+/bt7XQWAm2BUbeRr1+/TnR0NHK5nEWLFuHh4aF3ds2m1gRpaumFkpIStmzZwsGDB1m6dGk7nYVAW2C0NXJmZiZr167Fzs6ORYsW4enp2WhuY93Z51UYmpVek6KiIrZt20ZKSgrz58/Hzc2t3c9J4MExyhr56tWrLFu2jC5duqhrYhX6VjoCsLW11ZKxqZq5qKiILVu2kJ6ezvTp0+nWrVu7nYtA22B0NXJGRgbLly8nMDCQefPm4eLiAjReQFy3Zu7bty9+fn5606lQNSe2bt1KRkYGzz77LN27dzfJJW9NDaMSOSMjg2XLltG/f39eeuklJBKJ3oVtoLHMEolEvUqrIZnLysr45ptvuHTpElOmTKFHjx4PPOOnwKPFaJoW165dY8WKFQQHBzN79my6dOmi9yLO0EWeoX2q55WVlezYsYOTJ08ydepUevbsqTUvsiBzx8ZoauTNmzdz5MgRjh07xsaNG9v8+Eqlkh49evDmm2/i5+fX5scXaF+MRmSAjz76iMjIyEYxYtUD0FrKS7VNc7/mc8106enprF69WktiQ1EPgY6H0TQtVOhbb1lzm0Kh0Nqn+57mYsktjTMLdCyMSmTVbPWCzAK6GJ3I7Smzbl5NvRboWBiVyCpaI7M+IXVlbiqaIWActJvImZmZ7Ny5k+zs7DY9rqaELZHZkKytCc0JdHxaLXJlZSWbNm3iueee49SpUwbTZWZmEh8fj0wme6gCaqJPvraUWV9ehvYLdCxaFX67c+cOy5Ytw9bWFmdnZ8rKygymVe1TDatsK/R1P+suyatKp8LQSqe6vYKax9d9LtCxaVWN7OHhwffff8+KFSsQi8UG01VUVHDlyhWcnJxwdHRk06ZNDB48mMLCQhQKBatWrcLc3Bx/f3+effZZ3nnnnRYtOK6vZlVtVygUKBQK5HK5+rlubW2oGdGSiz6hVu7YtEsbuaamBktLS6RSKdHR0cTFxfGf//wHd3d33n77bQ4dOoRcLueHH36gpqYGFxcXXF1dmz2upsj6mgoxMTFMmTKFkSNHMnr0aEJCQrh+/breaIahpkhzoTmBjkm7iFxaWkpOTg4//vgjiYmJ/OMf/6BHjx5UVlbyz3/+k88++wwAJycn+vXr1+KxvvqE05QsNzeXMWPGsG/fPuLi4njqqafUC0w2J7O+fHS3CXRc2kXk8vJyLl68iLm5OV27dlWvIpqSkoJIJGL48OEA3L59m4aGhlatfafZXNB8yGQyysvL8fDwwNbWlrKyMmpra/H19dUbOzYkc0vjzAIdizYfayGXy7l58yY9evTg9ddfZ9u2bZw9e5aJEydSV1cHwL1796ipqWH79u3cuXOnxReEmhJqjqkAuHXrFoWFhVRUVFBTU8Pt27dRKpU888wz6vfqXsRpLsyu29TQvAAULvg6Pq0SuaKigm+++YbU1FRSU1O5efMmmZmZzJkzR93GrampISMjg27duhEWFkZCQgK7d+9m4MCBBAcH4+/vz4oVK5BIJNy5cwc3N7dW3UakK6GKu3fvYmlpiUQiQaFQIBaLEYlEVFZWIpFIGompeZymbocSamXjoFUiW1paEhQUhKenp7qmc3Jy0opgWFtbExkZiYWFBdbW1syaNYtr166pB7Z/9dVX3L59GzMzMxwdHRGLxdjb27cof82aU1fmwsJC7O3teeGFF/D19aWmpobQ0FAyMzPx8vJSv0efzIaaEYLMxkOrRLaxsWHcuHFNprG0tKRv377q1z4+Pvj4+ACwZ88eamtrmTVrFtevX+f48eNMnjy5xfnrCqeSub6+nry8PCwsLNQD7g8ePIiLiwvBwcGN4syGZFbloe/GVEHmjs0jHY88btw4/Pz8WL16NY6Ojrz22muMHj26VcfQFUokElFTU8Pdu3f5+eefiYmJwczMDBsbG3bs2IFEIgFoUmbNYxtqF1++fLl1JyvwSHmkIjs4OFBUVKR+bWZm1qoLKUNNgC5duvDGG2+wfPly9cB5MzMz9a1K+trVhmpZ3Z5DgOTkZNavX8++fftadb4Cj45HfoeI5n1wraWpkJhKXs07Rgxd3OmTWfO4qjT19fUkJyfz9ddfs3//fkaNGvXAZRdoX4zqVid48I6J5mTWPW5tbS2JiYnExMSwc+dOQeIOjlGJ/LCdFPou7lTbNfOQyWRcuHCB5ORkPvjgg1a34wUePUYnsqo2fdBIQlNtY7gfB79w4QLXrl1j6dKlPP300w/VHBJ4NBidyKqHZq9cazEkc01NDefPnyc7O5t58+YRERGBtbV1WxRdoJ0xKpFBu1Y21CvXEnRlViqV5Ofnc/XqVf7whz/wzDPPqMeICHR8jErkf//73+zdu1f9Wt/8FK15rbmturoab29vFixYwPjx4wWJjQyjmbG+uLi4yTtS2gKxWIy7uztWVlbtmo9A22M0IgsINIVRTgcgIKCLILKASSCILGASCCILmASCyAImgSCygEkgiCxgEggiC5gEgsgCJoEgsoBJIIgsYBIIIguYBILIAiaBILKASSCILGASCCILmASCyAImgSCygEkgiCxgEggiC5gE/w9/sMsqQhjmZQAAAABJRU5ErkJggg==)
Physics-General
Physics-
As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be
![](data:image/png;base64,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)
As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring balance will be
![](data:image/png;base64,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)
Physics-General
Physics-
Figures I, II, III and IV depict variation of force with time
I) ![](data:image/png;base64,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)
II) ![](data:image/png;base64,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)
III) ![](data:image/png;base64,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)
IV) ![](data:image/png;base64,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)
The impulse is highest in the case of situations depicted. Figure
Figures I, II, III and IV depict variation of force with time
I) ![](data:image/png;base64,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)
II) ![](data:image/png;base64,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)
III) ![](data:image/png;base64,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)
IV) ![](data:image/png;base64,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)
The impulse is highest in the case of situations depicted. Figure
Physics-General
Physics-
The variation of momentum with time of one of the body in a two body collision is shown in fig. The instantaneous force is maximum corresponding to point
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAAB+CAYAAADY39i+AAAPGUlEQVR4nO3deVDU9f/A8efKDaIcAoHG6YWKoKngGDmIqKMmNoaTxzhqNR55zGDS6MSMpeYxeDSOktlokyUMiRZ4lCgohhoEHhCxqEAJNqEQ4LLL7sLu749+MV8DjWQ/Lrv7fvyH8vnsa/Xp57N8/BwyvV6vRxAk0svYAwjmTQQmSEoEJkhKBCZISgQmSEoEJkhKBCZISgQmSMoggalUKhobGw2xKsHMdDuwtrY2vvvuO/bv32+IeQQz0+3Aampq+OKLLzh58iS5ubmGmEkwI9b//IXbt2/j7OxMTU0N9vb2BAUFYW9v3+nCra2tFBYWkpWVhVar5fLly4wdOxYHBwfJBxdMg9WmTZs2/f1FU1MTc+bMQalU8tVXX/Htt9/i6+tLUFBQpwvX19ezZ88e1Go1MpkMvV7P4MGDGTBgwHN7A0LP9tguUi6X09bWxqhRo0hLS2PKlCnk5eU9ceGbN2/i4+PDkiVLiImJYcqUKdy5cweFQiH54IJpeCyw27dvM3XqVCZPnoxer0etVuPt7f3EhZuamli9ejV+fn64urqyYMECvL29UavVkg8umIbHAsvPz8fR0RGZTEZJSQm5ublMmDDhiQtHRkby4osvtn/t4uJCeHg4ffv2lW5iwaQ89iG/vLycpqYmoqOjaWlpIT4+nsGDBz9x4X79+nX4NScnJ8NPKZis9sAqKyuxsrJizZo1uLu7I5PJ8PT0xNbW1pjzCSauPbDa2lpCQkLw8fHB09PTmDMJZqQ9sPDwcMLDw405i8lobW2lpaUFtVqNRqPh0aNH1NXVUVdXh42NDU5OTri6ujJs2DBkMpmxxzWqDgdahSerq6ujtraWW7duceXKFW7evMnPP//Mn3/+ibW1NW1tbdja2qLT6QgKCqKwsBA7Oztjj21UIrAuKCsro6ysjNzcXHJycigpKcHX1xcPDw/GjRuHm5sbffv2RaVS4ebmhkajwcvLy+LjAhHYU7W1tXH79m22bNnCiRMnUKlUxMTEsHbtWiIiIggICCAgIAAXFxd69RJnPnVGBPYE9fX1nDlzhq+//ppLly6hUql46aWX2LVrF0OGDBE/XXeRCKwTdXV17N+/n8OHDwOwePFiwsPDGThwICEhIUaezrSIwP6hubmZvXv3cuDAAVxdXdm4cSOxsbG4urqK3eAzEIH9w7Zt29i9ezdDhgwhKSmJyMhIsTvsBvFP8v/pdDo2bNjA1q1b8fX1Zd++fURHR3c5rra2NmJjY3FwcMDBwYGlS5cibvshAgNAo9Gwe/duduzYgZ+fH4cOHeLll1/+T+tITEzE29ubBw8e0NjYiEKh4Pbt2xJNbDrELhK4ePEiO3bswNvbm8TERCIjI//zOn777TecnZ2RyWTY2tqSlpYmwaSmx+K3YBUVFezduxeArVu38uabbz7TeubMmcO1a9c4evQoOTk5hhzRpFl0YLW1tezbt4+8vDzi4uJYtGjRM6/rtdde44MPPuD+/fusWrWKGzduGHBS02WxgbW1tXHmzBnS09MZPXo0q1at6vZhiFmzZvHhhx/i6elJVlaWgSY1bRYbWFlZGcePH8fW1pb169c/9cTKp7l37x6pqalUVlYCf13XcO/ePYYPH27IcU2WRX7Ib25u5tSpU+Tk5LBs2TLCw8Oxtn62PwpPT0/kcjnbtm0DQKlUsmnTJqKiogw5ssmyyMDkcjknT54kODiYOXPm4Obm9szrsrOz47333mPt2rXtx72cnZ2fOVhzY3G7yMbGRtLT0ykqKmLWrFmMHj262ycF2tvb4+LigqurK66uriKu/2FRgen1esrLy0lNTWXixIntR94F6VhUYCqVisOHD6NQKJg9ezahoaHGHsnsWVRgpaWlZGZmEhYWxtSpU409jkWwqMAOHDhAS0sLM2bMYODAgcYexyJYTGAFBQVkZGS0/+QoPB8WE9ju3btRqVTMnTuX/v37G3sci2ERgeXm5nL69GkGDRrE4sWLjT2ORbGIwD777DOam5tZtmwZzs7Oxh7Hoph9YHl5eZw/f54BAwawfPlyY49jccw6MLVaTUpKCo2NjSQkJFj8ZfzGYNaBFRYWkpOTQ//+/VmwYIGxx7FIZhtYc3MzGRkZ3Lt3jxUrVojPXkZitoEVFxeTk5ODr68v06dPx8rKytgjWSSzDEwul5OcnExpaSnDhw/H3d3d2CNZLLM8r6SgoIATJ06gUCjIycnh0aNHHW73WV1dzYEDB9rvou3l5UVqaqq4etvAzO5Ps7m5mcrKShQKBQ4ODkRFRdG7d+8O31dVVYVWq+X999/n888/p6amhlOnThlhYvNmdoFVVFRw7tw5xo4dy/nz50lJScHDw6PD91VVVWFjY0NYWBgKhYLKykqCg4ONMLF5M6vAVCoV2dnZXLt2jUmTJhESEtLpLk+n01FfX09ycjIjRozg1VdfJT8/n0GDBhlhavNmNoHp9Xru3r3L0aNHCQ0NZfr06U88NPHw4UPq6+vZu3cv+fn5DBkyRDw8QiJmE5hGoyElJQW5XM7kyZMZM2bME7+3vr4evV5PUFAQfn5+ODg4IJfLxc1KJGA2gRUXF3Ps2DFGjRrFwoULcXR0fOL3NjQ0PPaYnNDQUO7cufO8RrUoZnOYIikpicbGRtasWfOvF736+PgQExODl5cXALGxsbS2tj6PMS2OWQSWmZnJ2bNnCQ8PZ968ef/6n9q+vr74+vq2fz169GipR7RYJr+LrK6uJiEhgdbWVt5++21eeOEFY48k/A+TD2zXrl3cuXOHN954g9jYWGOPI/yDSQeWmprKsWPH6N+/Px9//LG4l2oPZLKfwUpKSkhKSkKpVHLo0KFO/ztIMD6T3II1NDRw5MgRqqqqWL16NdOmTTP2SMITmFxgTU1NpKSkkJ6eTlhYGCtXrhS7xh7MpAJTKpWcOnWKffv24ejoyOrVq8WzLXs4kwlMo9GQk5PDjh070Gq1xMfHM2nSJLH16uFMIjC9Xs+tW7fYvHkz9fX1vPPOO7z++uviPHsTYBKB3b9/n4SEBCoqKnjrrbdYunQpLi4uxh5L6IIeH9i1a9eYNm0aBQUFxMXFsX79evr06WPssYQu6rGBaTQavvzyS6Kjo7lz5w4LFy7ko48+eupZEkLP0+MOtOp0OhoaGoiPjyc1NRW1Wk1SUhLr1q0z9mjCM+hRgT169IiSkhKOHDlCZmYmGo0Gb29vEZcJ6xGBqdVqioqKyM7OJi0tjfv37zNhwgQ8PDwYP358p8vk5eUhl8vbv540aRL+/v7Pa2Shi4we2NWrV7lw4QKZmZncvXuX4cOHM2/ePOLi4ggICOhw0UZtbS3nzp3j+++/x83NDVdXV0pLS8nOzubdd98lLCzMSO9E6MxzD0yj0VBVVUVxcTE3btwgKyuLX375hWHDhrF+/XomT57M0KFDcXJy6rBsU1MTqampnD9/nvnz5zNjxgycnZ2prKxkyZIl7Ny5k2PHjj3vtyQ8xXMJrLm5mZ9++omCggIKCgqorKzk4cOH1NbW4u/vz8aNG5k+fTr+/v5PPXhaWlrKkSNHWLhwIbNmzWr/iTIgIIDx48eTnp7Or7/+ip+f3/N4W0IXdDswpVJJVVUVv//+O1euXEGr1VJYWEhmZiYKhQIvLy+qq6upq6tDoVCgUCgIDAwkOjqaV155hcjISPr16/evp9soFAqys7NxdHRk4sSJHQ5X2Nvbo1arqa6uFoH1IN0KTKFQsGHDBj799FN0Oh0ZGRno9Xp0Oh1arRYAmUyGg4MDERERTJkyhalTpxIUFIStrS1WVlZdvutNc3Mz+fn5+Pj4EBgY2OH3q6ursba2pm/fvt15S4KBdSswGxsbxo4dy+XLl1EoFISFhWFjY0NRUREVFRXodDrGjBnD6dOnO9x85L/SaDTU1NQwcuTIDg+vam1tJSsrCw8PD0aMGNGt1xEMq1uB2dnZsWjRIpycnPjhhx/Ys2cPAPn5+Wzfvh2lUsm6deu6HRdAr169cHBwQKvVotVqsbGxaf+9b775hgcPHrQ/GlnoOST5kD9u3DhOnDhh0HX26dOH6OhocnJyuH79OuPGjQP+ijkhIYGZM2cye/Zsg76m0H1GPw7WVc7OzixcuJCqqioOHTpEUVER8Nc98GNiYjh48KCRJxQ6YzKBAQQFBZGYmMi5c+dITU2luLiY5ORk8WiYHkzywFQqFWlpaVy4cAGAwYMHs2jRoseurP4vAgMDWb58OQ0NDZSXlzNgwABxV8IeTPK/mZaWFkpKSggPD2fp0qVUVFRw9uxZVCpVt9Y7c+ZMfHx8WLFiBVFRUSQnJxtoYsGQJN+CtbS0UF5ezpIlSxg2bBgXL15EpVLR1tbWrfUGBweTkZHRHqo4w7VnkjwwrVZLXV0dwcHBFBQUUFNTQ0xMTLcvlLWyssLHx8dAUwpSkTywq1evcuvWLXx8fOjTpw+bN29mwoQJUr+s0ENIHphcLmf79u2sXLlS6pcSeiBJP+T/fd/UkJAQKV9G6MEkDUwmkxEaGkpQUJCULyP0YJLvIuPj46V+CaEHE0coBUmJwARJicAESYnABEmJwEycXq9HpVLR3Nxs7FE6ZVKn6wgdtbW18eOPP1JWVkZERAQBAQE96roEsQUzcdbW1kRERODi4kJCQgJJSUlcunRJki2aVqtFLpdTVlbW9fkM8cJWVlbcuHGDnTt3GmJ1wjNQKpUolUq2bNnC8ePHiYuLY/ny5QY9IeDvW5i6u7szdOjQLi1jkMBCQ0OZO3eueN6PEclkMpydnXFwcMDJyQkrK6t/faTOf9Ha2sonn3xCRkYG7u7ueHh4MGPGjH9dziCBBQQEsGLFCkOsSngGarWarKwsrl+/TmJiIlFRUQwfPtygzw7o1asX/v7+1NfXs2zZsk6vTe2M+JBv4nQ6HRUVFSiVSjZu3Iifnx+9e/c26NYL/tpC+vr6MnLkSObPn4+1ddfSEYGZuF69ejFo0CACAwOxtbU1eFh/0+l0lJaW4ufn1+W4QPwUaRasra2xs7OTLC7463jbH3/8gZeXV/ttIbpCBCZ0iUwmw8fHh4MHD5KYmNj15fTiQdWChMQWTJCUCEyQlAhMkJQITJCUCEyQlAhMkJQITJCUCEyQlAhMkJQITJCUCEyQlAhMkJQITJCUCEyQlAhMkJQITJDU/wFuQCkFBGPb3QAAAABJRU5ErkJggg==)
The variation of momentum with time of one of the body in a two body collision is shown in fig. The instantaneous force is maximum corresponding to point
![](data:image/png;base64,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)
Physics-General
Physics-
A body of mass 3kg is acted on by a force which varies as shown in the graph below. The momentum acquired is given by
![](data:image/png;base64,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)
A body of mass 3kg is acted on by a force which varies as shown in the graph below. The momentum acquired is given by
![](data:image/png;base64,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)
Physics-General
Physics-
A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is a semicircle.
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)
A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is a semicircle.
![](data:image/png;base64,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)
Physics-General
Physics-
A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F0 linearly in time T/2, and decreases linearly to zero in further time T/2. The magnitude of F0 is
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)
A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F0 linearly in time T/2, and decreases linearly to zero in further time T/2. The magnitude of F0 is
![](data:image/png;base64,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)
Physics-General