Physics-
General
Easy
Question
The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with above spring of half length, the line
will
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAACwCAYAAAB5Ej47AAAV40lEQVR4nO3da1BTd/4/8HdARCgiVlvZuqz4wC3dUkTkEggkEMFSL22HmZ2uM+12Z92dfbCQm7Czs+POdGe6avcBoFRFEMWO1XpDEJAIZtWyWgcFwi1BrKV2WSshCQnhFhLI78H+OX9ZFRBCTi6f10NCzvlE3/Pl5Hw/3+/h2Gw2GwhxQV5sF0DIXFF4icui8BKXReElLou18I6OjmJgYICt0xM3wEp4rVYrGhoacP78eZhMJjZKIG6AlfD+8MMPqKysxJkzZ9DW1sZGCcQNODy8k6OuQqGASqVCTU0NhoeHHV0GcQMOD++PP/6IW7duoaOjA48fP4ZCoYBarXZ0GcQNODS8ExMT+Ne//oXbt2/DarXCarXi4cOHqKyshNlsdmQpxA04NLw6nQ719fX4z3/+g5UrV8LPzw82mw0VFRV48OCBI0shbsBh4bXZbFAoFOjq6kJaWhq2bt0KLpeL3bt3w2Aw4OLFi5iYmHBUOcQNLHLUiYaGhvD1119j3bp1+P3vf4/bt2/DZDJhx44d8Pf3x549e/Dhhx8iJCQEXl40d0Jm5rCU3LhxA+Hh4di5cyfeeustAACHw8GyZcuwfft27NmzB2fPnsXY2JijSiIubtYjr81mw69+9St0dXXBarVOeY3P5+MPf/gDIiIinvv+pUuXQigUYu3atfDx8WF+7uXlheXLlyM1NRVtbW3o6+vDT37yEyxa5LA/CsRFzSohExMTePz4Merr6yEQCJCRkYGVK1cyr69YsQKhoaHTHmP9+vVYsmQJfH19n3rNy8sLy5Ytw4YNG7Bo0SJ4e3u/4McgnmjW4X306BGGh4eRlJQEoVCIFStWvNCJli1bNu3rHA4HAQEBL3RM4tlmdc1rtVqhUqkwPj6OkJAQLFmyZKHrImRGswqvxWLBrVu3EBAQgNWrVz/zTz8hjjbrkbelpQVhYWF45ZVX6MsUcQozpnBiYgImkwnd3d148803UVNTM+X6NSIiAm+88caCFknIs8wY3rGxMXz77bfo7e1FcHAwTp8+PeVuwM6dOym8hBUzhtdsNkOtVoPD4eAf//gH+Hw+fWEjTmHGa16LxYKenh54e3tj1apVdA+WOI0Zwzs8PIw7d+5g7dq1WLNmzZTZMULYNGN4h4aG0NDQgOTkZAoucSrThtdsNuPHH3/ExMQEQkNDqduLOJVpv7D5+PggKioKCoUCP/3pT2lygjiVacPr5eWFoKAgxMXFOaoeQmaNrgOIy6LwEpdF4SUui8JLXBaFl7gs6m0ks2Y0GuHl5QU/Pz+naItlvwLiEgYHB1FTUwMOh4PY2FisWbOG9UkrumwgM7JYLDh37hw+++wz/PGPf8SFCxecYmtaCi+Z0cmTJ5GbmwuVSgU+n4/ExEQEBgayXRZdNpDns1gsTHDv37+P7du3QyqVIioqChwOh+3yKLzk2QYHB3Hu3LkpwZVIJIiKisLixYvZLg8AhZc8Q39/P8rLy1FQUICurq4pwfXz82O7PAaFl0zR19eHyspKHDlyBPfu3cOWLVsglUqxceNGp1v+ReEljMePH+Py5csoKSlBV1cXUlNTkZ2djZiYGKe5VHgShZcA+G9wq6urUVpaiq6uLvD5fMhkMsTHx7N+P/d5KLyEGXFPnDiBrq4uJCQkQCQSQSAQsF3atCi8Hk6j0aCmpgalpaW4d+8e4uLikJmZiU2bNr3wsWw2G4aGhnDt2jVYrVYIBAK8/PLLC1D1fznn3wPiEHq9HlVVVSgpKYFarQaXy0VWVhbS0tLmdLyxsTHU19djx44dyMjIQHNz81N7OdsThddDmUwmVFRUoLi4GCqVCvHx8fMK7sTEBPr6+vD3v/8dy5cvx6JFi3Dv3j0YjUY7V/7/UXg9kNlsRllZGQ4ePIj29nYkJiZCKpUiNTV1zsccGhpCfX09mpqasG/fPqxcuRJarRajo6N2rHwqCq8H+uqrr5Cbm4vW1lYIhULk5OQgJSVlXsd89OgR/va3vyElJQXvv/8+AgICoNFoKLzEPmw2G06cOIHc3Fzcu3cP27ZtQ05ODrhc7ryO29PTgxMnTsBgMGDv3r1YsmQJVq9ejc7OTuj1ejtV/zQKr4cYHR3FF198gdzcXHR1dWHr1q2QSqWIjo6e905I33//Pc6ePYv3338fYWFh8Pb2RkhICPr6+jA0NGSnT/A0Cq8HGBgYwJkzZ5CXl8dM+UokErtM+XZ1deH06dOw2Wz4+OOPmZm49evXw2QyYWRkxB4f4ZkovG5Op9MxX87UajXeeecdJrj+/v7zOvbw8DDu3r2Lb775Br/85S+xfv165rXQ0FBwOBw8fPhwwe440CSFG9NoNLh8+TKKi4vR2dmJzZs3QyaTISYmxi5NNmq1GpcuXcKDBw/Q0NCA7Oxs5rWHDx9Cp9Ph0aNHGBgYmPFpUHNB4XVTvb29qKmpwbFjx6BWqyEQCJCTk4P4+Hi7LJ40Go24efMmHjx4gIyMDKxdu3bK6/7+/mhuboZer8fw8PC8z/csFF43NBnc0tJSqNVqJCQkQCKRgM/n2+0czc3NuHbtGlavXo2//OUvWLdu3ZTX+/v7cePGDTx8+BAGg8Fu530SXfO6mSd7FVQqFbhcLsRi8Zx6FZ5Hr9dDoVCgu7sbSUlJTwUXAJYvX45Vq1ahp6cHOp3Obud+Eo28bkSn06GmpgbHjx+HWq1GbGwsMjMz5zzlO915Fi9ejPT0dKSnpz/397Zs2QKlUomlS5fa9fyTODabzbYgR57BoUOHcP36dZw9e5aN07sdo9GI8vJyFBcXQ61WIz4+HiKRCJs3b2a7tAVDI68bGB4eRkVFBQ4fPgy1Wo2kpCRIJJJ59Sq4Agqvi5uYmMCFCxewf/9+dHR0MEt3kpOT2S5twVF4XdzJkyeRl5cHtVqNt99+GzKZDDwej+2yHILC66KsVitOnz6NvLw8dHZ2MjNncXFxTrEJniN4xqd0M0NDQygrK0Nubi4TXLFYbLeZM1dB4XUxBoMBly5dQkFBAdRqNdLT0yEWixEdHT3vXgVXQ+F1IVqtFpcvX0ZhYSE6OjqQlpYGqVSKmJgYjwsuQOF1GZMzZyUlJVCpVEhJSUF2dja4XK7HPh+PwusCent7ceXKFRw/fhwqlQo8Hg8ymQxJSUlOuyGII1B4nZxGo5kS3NjYWLv3KrgqCq8T02q1kMvlOH78ODo6OhATE4OsrCy3nvJ9EZ77N8fJGQwG5hq3ra0N0dHRyMrKmrYRxtNQeJ3Q0NAQqqqqcOTIEbS0tDCXChTcqeiywclYLBZcvHgRBQUFaG9vh0AggEwmc/smm7mg8DqZs2fPIi8vDx0dHdi0aRNycnLsugLCnVB4nchkk41KpcLmzZshlUqden9ctlF4nYDZbMb58+endIeJxWLExcV57ATEbFB4WWYymXDp0qUpI65YLEZsbKxHTvm+CAovi/r7+1FdXY2DBw+ira0NmzdvhkQiQWxsLF566SW2y3N6FF6WTE5AFBUVob29HUKhEDKZDFwu16keF+XMKLws0Gg0qK2tRUlJCdrb28Hj8ZCTk4PExMR5b3rnSSi8DvZkr0J7ezvi4uIglUohFArZLs3l0D0YB9JqtaitrUVpaSna29sRHR3t9svTFxKF10H6+/shl8tx7NgxtLa2YuPGjcjKysI777zDdmkuiy4bHMBkMjG7Nba1tSE2NhYikYiCO08U3gVmNptRWVmJQ4cOobW1FTweD1KpFG+//Tbbpbk8Cu8CKysrQ15eHlpbW5GSkoKcnBxqJLcTCu8COnXqFPLy8tDe3s4slkxKSmK7LLdB4V0A4+PjzDMgJlf5isViJCQkOOXT010VhdfOJje9mwxuamoqxGIxzZwtAAqvHRmNRlRXV+PAgQNoa2tjRty4uDjqVVgAFF470ev1kMvlKCwsZL6cTY64FNyFQeG1g8mZs+LiYrS0tCApKQnZ2dng8XgetXeYo1F456mvrw91dXUoKSlBa2sruFwudu3aheTkZHh7e7Ndnluj8M6DVqtFXV0dM+UbHR0NsVhMvQoOQuGdI71ez7Q1tra2IioqCiKRCFu2bGG7NI9BjTlzMDAwALlcjqNHj0KpVGLDhg0QiUTYunUr26V5FBp5X9DIyAiqq6tRWFiIlpYWxMXFQSKR0IjLAgrvCxgfH8elS5dw4MABKJVKJCYmYteuXdRkwxIK7ws4d+4c02STnJwMmUyGlJQUtsvyWBTeWfrqq6+YJptNmzZBLBYjKSnJYx5e4ozoX34GY2NjuHjxIhNcoVAIkUiEhIQEmoBgGYV3GoODg6iqqkJ+fj7a2tqY4MbHx9OUrxOg8D6HwWCAXC7HwYMHoVQqIRQKIRaLER8fj4CAALbLI6DwPpNOp0NtbS2KioqgVCqZZ/nyeDzagsmJUHj/h1arxdWrV1FSUgKlUgkul4ucnBwkJydTI7mTofA+4X+DGx0dDZlMhrS0NHA4HLbLI/+Dwvv/6PV6XL16FceOHWOmfMViMS1Pd2LU24D/roCora3F0aNH0djYiPXr10MkEmHbtm1sl0am4fEj79DQEORyOY4cOQKlUomNGzdCIpFQcF2AR4fXYrGguroan3/+OZqbm8HlciGTyajJxkV4dHgnZ86am5uZpTtpaWlsl0VmyWPDe+bMGeTn5zOLJSUSCZKTk+nhJS7E48I7MTGB8+fPM1O+ycnJEIlESExMpIeXuBiPCu/IyAiqqqqmtDVONtlQr4Lr8Zjwmkwm1NTU4MCBA2hpaUFycjKysrKQkJCApUuXsl0emQOPCG9/fz/q6upw+PBhNDY2IikpiblUoCYb1+X24dXpdFAoFCgqKkJTUxPi4+Mhk8kgEAho7zAX59bh1el0zJRvU1MToqOjsWvXLqSmptIKCDfgtv+DkyPusWPH0NjYiMjISFrl62bcMrwGgwEKhQJHjx5FU1MTIiIiIJFIsH37drZLI3bkdnfkBwcHUVdXh6KiIty9excREREQi8V499132S6N2JlbjbxmsxlyuRyHDh1CY2MjoqOjIZVKacR1U24V3srKSuTn5+Pu3buIj49HdnY2XeO6MbcJ77lz55Cfn4/m5mbw+XxIpVKkpqayXRZZQG4R3sngtrS0QCAQQCQSQSAQ0EOo3ZxLh9disaCiooIJLp/PR2ZmJhITE2mVrwdw2fAODQ2hpqYG+fn5UCqV4PP5yMrKAo/Ho14FD+GS4TUajairq8Pnn3+OxsZGJriJiYkUXA/icuHt7++HQqFAYWEhc1dBLBZDIBBQW6OHcanw6nQ6XLt2DcXFxcx93OzsbGzatIkayT2Qy4RXr9fjn//8J0pKSnD37l1ERkZCJpMhPT2dlu54KJcIb39//5TgvvXWW9SrQJy/t2FgYAAKhQLFxcVoaGhAeHg4JBIJ3nvvPbZLIyxz6pF3ZGQEdXV1KCwsxJ07d7BhwwZIpVIKLgHgxOEdHx9HTU0NCgoKcOfOHcTExGDXrl10qUAYThve8vJy5Ofno7GxkVm6Q0/dIU9yyvBeuHCBabJJTEyEWCyGUCikpTtkCqdKg81mQ1lZGTPlm5iYiKysLFosSZ7JacJrNptRXV2N/fv3Q6lUgsfjITMzE0lJSbQ8nTyTU4R3cHAQtbW12L9/PxobG5ng8vl8BAYGsl0ecVKs3+c1GAy4cuUKDh06hIaGBnC5XKYfl4LrOb7//ntcuXIFWq121u9hNbx6vZ7ZEKShoQGxsbGQSqUQCoXUHeZhOBwONBoNSktLcf78efT09Mz4Hu9PPvnkEwfU9pQ7d+6gsrISPT09aGhoQEREBHJycpCenk5PlvRAQUFBWLZsGa5cuYLa2lr09PRgZGQEvr6+CAoKeuZ7WAlvf38/rl+/jqqqKmi1WoSHhzMzZ97e3o4uhziJoKAghIWF4f79+zh16hTq6+sxPDwMDocDDofzVIhZ+cL273//G9999x2sVit8fX0RFxeHVatW4datW2yUQ5xMXFwclEol6uvrsXfvXnz55Zf44IMP8NFHH+H1119nnofHsdlsNkcXZzKZ8MUXXyA/P5+eb0aeMjY2Br1ej8HBQQCAr68vXn75ZcTGxuLw4cMIDg4GwFJ4Jwu0Wq20UJJMMT4+DqVSiX379kEul8PHxwcbNmzARx99hPT0dCa4AIvhJeRZWlpasHv3bty8eROxsbH4+OOPkZKSgldfffWpRQcUXuI0lEol9u7dC19fX2zZsgVcLhfBwcFYvHjxM1fLUHiJU/j2229x+/ZtBAUF4fXXX0dwcDD8/f2nvftE4SVOQaPRYGxsDIGBgXjppZdmdcuUwkucgsViwaJFi17o7hOFl7gsu01SdHZ24vLlyzCZTFN+/tvf/havvfYazZwRu5t3eHU6HZqbm1FXVweVSoU1a9YAAKxWK7755huMjIwgIyMD4eHhdE+X2NW8wjs4OAiFQoELFy7A19cXmZmZzDozi8WCL7/8Ert374bZbIZYLEZoaKhdiiYEmGdLZHNzM86cOQM/Pz/8+c9/nrJA0sfHB7/5zW8QGRmJmzdvQqPRzLtY4j7MZjMePHjANN9MfvXq7+9HY2Mj2tvbYTQapz3GnMM7PDyMsrIyaDQapKam4he/+MUzfy8iIgLd3d0zFkI8i8FgwKlTp7Bt2zaoVCpYrVZYLBbI5XKIRCLs378f3d3d0x5jzuFtaGiAUqlEaGgoIiMjn/t7ExMT8PLyogYcMkVQUBAEAgG8vb1x8eJFmM1m3L9/HwUFBQgODsbOnTunzRUwj/B2dnZCo9HgzTffRHh4+HN/r6enBytXrqTVv2QKX19fhIWFISMjA/v27YPRaER2djYWL14MqVQKLpc74zHmHN729nYEBgYydxee54cffsArr7xC4SVPCQgIwPbt28HhcBAeHo6rV6/iT3/606yCC8wjvOPj4+BwOM/dXnR8fBxNTU347rvvwOfz8eqrr871VMRN+fn5gcvl4mc/+xlMJhM+/fRTbNy4cdabyyzYAkyr1Yrq6mqYTCYIhUKsWrVqoU5FXJROp8Onn37KTGB1d3djeHh41u+fc3iXL18Oi8XCdLs/aXR0FF9//TVOnjyJDz/8ED//+c/psVJkit7eXhQVFaGqqgp//etf8e677+L69etQq9UYHR2d1THmHF4ej4fAwEDcuHEDTU1NzM+NRiMqKirw2WefITw8HDt37sSKFSvmehrihjQaDcrLy1FeXo5f//rXeO+99/C73/0OIyMjaGhomPXeDXNuzNFqtaiurkZFRQUAICwsDMB/R93e3l5ERkaCx+MhOjqaWTBHyODgIK5evYqCggKEhIRgz549eO2112A0GrFjxw4YjUbs2bMHAoFgxmPNeem7v78/1q1bBz8/PwwODmJ8fBzj4+Pw8fFhtt0PCQmhhhwyhdlshk6ng7e3Nz744AO88cYbAIAlS5bA19cX/v7+iIqKmrJW7XmoJZK4LNb3KiNkrii8xGVReInLovASl0XhJS6Lwktc1v8BF/HQE51XVbsAAAAASUVORK5CYII=)
- Shift towards F-axis
- Shift towards X-axis
- Remain as it is
- Become double in length
The correct answer is: Shift towards F-axis
When the length of spring is halved, its spring constant will becomes double
![open square brackets B e c a u s e blank k proportional to fraction numerator 1 over denominator x end fraction proportional to fraction numerator 1 over denominator L end fraction therefore k proportional to fraction numerator 1 over denominator L end fraction close square brackets](data:image/png;base64,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)
Slope of force displacement graph gives the spring constant
of spring
If
becomes double then slope of the graph increases
graph shifts towards force- axis
Related Questions to study
physics-
Two small particles of equal masses start moving in opposite directions from a point
in a horizontal circular orbit. Their tangential velocities are
and
, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
, these two particles will again reach the point ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Two small particles of equal masses start moving in opposite directions from a point
in a horizontal circular orbit. Their tangential velocities are
and
, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
, these two particles will again reach the point ![A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
physics-General
maths-
In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is
In a model, it is shown that an arch of abridge is semi-elliptical with major axis horizontal. If the length of the base is 9 m and the highest part of the bridge is 3 m from the horizontal, the best approximation of the height of the arch, 2 m from the centre of the base is
maths-General
maths-
The number of non-negative integral solutions of x + y + z n, where n N is -
The number of non-negative integral solutions of x + y + z n, where n N is -
maths-General
maths-
Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -
Between two junction stations A and B there are 12 intermediate stations. The number of ways in which a train can be made to stop at 4 of these stations so that no two of these halting stations are consecutive is -
maths-General
maths-
If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -
If n objects are arranged in a row, then the number of ways of selecting three of these objects so that no two of them are next to each other is -
maths-General
Maths-
The number of numbers between 1 and 1010 which contain the digit 1 is -
The number of numbers between 1 and 1010 which contain the digit 1 is -
Maths-General
Maths-
The number of rectangles in the adjoining figure is –
![](data:image/png;base64,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)
The number of rectangles in the adjoining figure is –
![](data:image/png;base64,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)
Maths-General
chemistry-
Assertion :this equilibrium favours backward direction.
Reason :
is stronger base than ![C H subscript 2 end subscript C O O to the power of minus end exponent](data:image/png;base64,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)
Assertion :this equilibrium favours backward direction.
Reason :
is stronger base than ![C H subscript 2 end subscript C O O to the power of minus end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAARCAYAAACcsPEBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAeNJREFUeNrtmEFERFEUhsczkhbRMkmMkbRIm6RFEq3Sok2LVkm0SIsWkSQt2qVVu5EnSSLJLEabjLSYbZIk0SKtEiMjGW3qP5zHk3fvO+e+GUrz863O75y51z33njepVLQyYAtcgw/wBDZB2w8fxTxDDlssTtL6pD7ggxdQAfug15Jb6v+yYNQyKIDh0OI7wRLYC/my4MaQwxaLk7Q+aR3kwQB7iUne7MGI3Fq/SitgV+ilokcOsVrVXwM5Q2yUT20Sv0rd4BGkhf4NXqw2Vov65L2PuRYqoTbX+tXa5taQ6phPmDZWi/rkXYzxnHPru/jVuuO7SqqHmEu1o471b0FXjOcZtDr6VaLjXFX63w2xNL+Q9arvCfLTb3hz9KvVxD0vFb1MRUNsCFzUsb7EOwUOHP1OopPUIvROR4wNtljQyp+gZGhPaX2P89gu/1Jo9ND6neTzjCXRDpizxOYtC18AVwnr0xw4a4itRowkWr9adKGWOVnwZDeDCV7YWMh7CsYNefKWWKBqwvpZHj1mQqNNP7dezjC0a/xOyvLnSoXbjC7Rk4jNKPPComSLkUbAZcL6wVeHz/VewSHftyZp/b9O7Xy/ZFINqb8gCryBDSlP3JnrEPrfRRvX09gGN6n+E/sr+gYWspix7n20kAAAALl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bXJvdz48bWk+QzwvbWk+PG1pPkg8L21pPjwvbXJvdz48bW4+MjwvbW4+PC9tc3ViPjxtc3VwPjxtcm93PjxtaT5DPC9taT48bWk+TzwvbWk+PG1pPk88L21pPjwvbXJvdz48bW8+LTwvbW8+PC9tc3VwPjwvbWF0aD6kqiZ7AAAAAElFTkSuQmCC)
chemistry-General
Physics-
A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904353/1/923693/Picture33.png)
A 0.098 kg block slides down a frictionless track as shown. The vertical component of the velocity of block at
is
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/904353/1/923693/Picture33.png)
Physics-General
physics-
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are
respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
,these two particles will again reach The point ![A ?](data:image/png;base64,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)
![](data:image/png;base64,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)
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are
respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at
,these two particles will again reach The point ![A ?](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position
are
The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486211/1/923664/Picture20.png)
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position
are
The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486211/1/923664/Picture20.png)
physics-General
physics-
The potential energy of a particle varies with distance
as shown in the graph.
The force acting on the particle is zero at
![](data:image/png;base64,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)
The potential energy of a particle varies with distance
as shown in the graph.
The force acting on the particle is zero at
![](data:image/png;base64,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)
physics-General
physics-
A
mass moves along
-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from
to ![x equals 8 blank c m](data:image/png;base64,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)
![](data:image/png;base64,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)
A
mass moves along
-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from
to ![x equals 8 blank c m](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A mass
slips along the wall of a semispherical surface of radius
. The velocity at the bottom of the surface is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPgAAACjCAYAAACnmNM/AAAU/ElEQVR4nO3df2gT9/8H8Ge377Y47ZqNDeM2aBxUb8hoBJmpOBr/asRhEhmzwqDNFNqgWAu62v2T9g+NzkFbUNIKknZjNIWxtIXR9A9NCoJRJ41so6kOvKCu2WD21GJvOrjvH+Xu0/RHekkuueT6esCHz5q73L1M7pX3+96/rkQQBAGEEE16Se0ACCG5QwlOiIZRghOiYZTghGgYJTghGkYJToiGUYITomGU4IRoGCU4IRqWdoIPDw+jpKQEJSUlOHToEADg1q1b2LRpE0pKSjAzMwMAuHPnDvbt24eSkhJMTU0pGzUhRJa0E3zv3r0QBAEVFRWwWCwIh8N4+PAhLl68CAAYHBzE1NQUfvzxR3z33XcAgJ9++knZqAkhsmRURb9z5w7u3r2L999/H0+ePMHevXvx4MEDAMAbb7yBy5cv4+uvv8bk5KSiwRJC0pNRgt+4cQMVFRX4/fffsXfvXgBAOBwGADx58gR2ux0AMDo6CgDYsmWLErESQtKUUYKLVe59+/ZJr126dAk7d+7Exx9/jHXr1gEARkZGAAAWiyXbOAkhGUg7wWdmZhAIBGCz2bBhwwYAc41sAPDOO+9g06ZNAICpqSlcvXoVx48fVzBcQkg60k7wX375BQCwZ88e6bVIJAIAOHr0qPTazZs3F+1HCMmvtBP8559/BpBc7b58+bLUqi4aHh4GAGzbtk3qOiOE5FfaCT40NJRU7Rar7PX19Un7Xbp0CQcPHkRfX1/2URJCMpJWgovdY5988on0mlhl37Fjx6L9Hz16hH379kmNboSQ/CqhNdkI0S4ai06IhlGCE6JhlOCEaBglOCEaRglOiIZRghOiYZTghGgYJTghGkYJToiG/d9KOzx//hwvXryQ/l67dq3034Ig4NmzZ9LfL7/8MnQ6nfT3f//9h3///XfJbYSQPBCWMT09LZSWlgpvv/22ACDr/23YsEGYnZ2Vjl9fXy9tYxhm0fkZhpG2NzY2Jm2bmJgQ9Hq9tL2joyNpe39/v7RNp9MJoVAoabvH45G2GwwGYXp6Omm71WqVtptMpkWfi8FgkLYfO3YsZWz9/f3LxqbX64Vr164lbW9sbEyKbf5ntjA2q9WaMja32y1tGx8fF86ePSvodDppeyAQSHq/z+dLim1iYmLZ2Fb6zux2e8rPxePxJG0PhUJSbCt9Z3q9Xrh3796yn8vC72xhbCtdT16vN2n7wutp4XeWzvVksViStq10PY2Pjy95PXm93kXXxlKWLcF1Oh2ePn2Kp0+f4tdff5X3a7GMP//8E19++SVeeul/dwQ2mw3l5eUAAIPBsOg9DQ0N4DgOAGAymZK2GY1GtLS0gOd5AItXjDGbzXC73dLfDMMsu12n0y2qWTQ0NGD79u3SuebT6/VoaWmRYlt4boPBgKampmXPzTBMytj279+P9evXS+daGNv+/fuXjU2n06GpqWnJz6Wrqwt//PEHWlpapNcWfq4mkynpc1n4vdTU1CTFtlBLSwtYll3y2Ct9Z+L2+X/PZ7VapfcuFVuq70zcvtz1tPA7M5vNSduzvZ5SfWcrXU9GozEpNjH2b775Blardcl/63wpJ5ts3LgRLMsqkuAHDx7E/fv3szoOyZzT6QTLsgiFQmqHQhTwwQcf4MqVKysmODWyEVKEEomEVJtKJWUj21LVMFKcWlpakEgk1A6DKITneVmN1nlLcEEQ8Pz5c7z66quKHZPIxzDMontHUpw4jpOdmymr6Ep2awmCkNTdRgjJDMdxKCsrk7VvygRfqnWbEKIuudVzgBrZVo1wOAy/3692GEQBiUQCBoMBJSUlK+6btxK8pKQEr7zyimLHI+np6+tDT0+P2mGQPEuZ4K+99ppiJyopKaEGNkIUwLLsiv3forw1shFC8i9lNxk1smnH/OGQpLil002WtwSnfnB1UR+4dkxOTqKyslLWvimr6HLr+XJQPzghyohGo4smzCwnZYLTrz4hhWdychKbN2+WtS/1g68S1A+uDYlEAjqdTpl7cABYs2YNPvroo6wDe++996hVXkV9fX1gWRa1tbVqh0KywLIsysvLZQ1yAWQkeFNTE8rKynDy5MmsgyOEZCed+29ARhW9vLwc8Xg8q6CI+qj2pA3p3H8DMkpwk8mEvr6+rIIi6pu/XBIpXrFYDDU1NbL3XzHBjUajtM4WKV5KdnkS9dy+fVt2Hzggo4puMBjA87zsUVB+v59KCkJyQMzDdAagyeomYxgGsVhM1gGbm5tpSCQhORCLxdK6/wYUTnCO48DzPI1hL0DUD178wuEwLBaL7C4yQGaCV1dXY2xsbMX90pnGRvKL5oMXv7GxMVRXV6f1HlkJbrFYEA6HV9wvFovR8FZCcoDneYyNjaXVgg7ITHCxVF6pNT2daWwkv6gfvLhFIhFUVlZizZo1ab1P9lh0OaW4wWCgtbcLVEtLC7xer9phkAyFw+G0q+dAGgku5z5cr9dTC3qBMhqNdPtUxIaHh2G329N+n6IlOA2KIUR5HMeBZdm0BriIZCe4nPtwvV4PnudpoAshChKr5+l0j4nSmg++Uimu1+vBMAwikUjagZDcGhwcRHd3t9phkAwMDQ3BZrNl9N60ElzOfbjNZsPQ0FBGwZDcGRoawsDAgNphkAyIA1wyoWgJDgB2ux2Dg4MZBUMISSbeEpeXl2f0/rQS3Gg0guf5lF1hRqMRer0e0Wg0o4BIblA/eHHy+/2ora3N6P4bACCkqbGxUfB6vSn3CQQCgt1uF6anp4UdO3YIs7Oz6Z6GKGx6elq4d++e2mGQNDEMI0xMTGT8/rQXXdy/f/+K93J2ux08z+PixYu4efMmjh49mtmvD1GMXq+neQJFJhKJSA3XmSoRBEFI900bN25EKBRKecFEo1Hs3r0bHMfh9ddfxw8//ACr1ZpxoISsNi6XC5WVlWhsbMz4GBktm1xbW5ty6mE4HMapU6fw5MkT8DyPR48e4dChQzSMlRCZeJ7H4OBg1qvgZpTgdXV1y67Tlkgk8Nlnn2FwcBDPnj2TXv/7779RX1+fWZQka36/H2fOnFE7DCLT4OAgLBZL1pO3MkpwhmGg0+mWbCk3GAx48OABPB4P3nrrLaxduxYA8OLFC9y4cQPff/99VgGTzIyOjmJ0dFTtMIhMfX19qKury/o4GT/ZJFVjm06nw/Hjx/Hw4UO0tbVJiT49PY2vvvqKquqEpJBIJBCNRhVps8o4wevr69Hb25tyn6US/Z9//sGePXsyPS3JkE6no77wItHb26vc7Ww2fXQWi0UIhUKy95+dnRXOnTsnvPnmm0J/f382pyZpon7w4pFt3/d8GXWTzf+lGRsbg8/nS+t94mwzKlEISRaJRNDc3Ixr164pcrysEpzjOHz44Ye4d+8eJSshCnA4HKirq8tocYelZPX4YL1ej9raWpqGSIgCotEoWJZVLLmBLEtwYK7Fr6qqChMTE1SKF7Du7m7E43F4PB61QyHLULr0BmQ8m2wlBoMBJpMJwWBQ0cCIsq5fvy57Oa3h4WHcv39/0etbtmzBtm3bsG7dOqXDW/VyUXoDWVbRRW63G+3t7UocihSAJ0+e4MiRIzhy5Ig0JJllWezatQulpaW4c+eOyhFqT3t7O9xut+LHVSTBTSYTjEYjLfRQwNLpB//iiy9w/vx5AMCJEydw+PBhnDt3DpOTkwCATz/9NGdxrka5Kr0BZNcPPt/4+LhgMpmUOhxR2OzsrDA9PS17/1OnTgkAhKdPnya9DkBQ8LIhgiDY7XYhEAjk5NiKlODAXCmu1+tlPeKI5J9Op0tr4kJvby8OHjyYdL89NTUFAKioqFA8vtUqp6U3FKqii5qamtDV1aXkIYkK7ty5g7t372Lv3r3SazMzM/j8888BAN9++61aoWlOru69RYomuN1uB8uytB5bkbtx4wYA4LfffsOFCxdw4sQJlJaW4urVqxgaGkpKfJK5XJfeAJS/mRLXYyOFxev1CidPnpS1786dO4WKigrh/PnzgsPhEAAI58+fz3GEq4/VahVGRkZyeg5FS3CASvFCdf36dVkPpJiZmcHVq1dhs9lw+PBhaZEIeiSVsvx+P/R6fc6XMVM8wQHA5/PB6XTm4tAkx65cuQIA0pTeTZs2oaKigu67FcTzPFpbW9HR0ZHzc+UkwU0mE8xmM41RLyB6vV5WP/jw8DAAYNu2bdJr4txk6iFRRmtrK5qammAwGHJ/slzV/aempgSTySRMTU3l6hQkBwAIO3fuTHptcnJSACAcP35cpai0I9/jRXJSggNzY9QbGhpoCGsREUvvhSt5zq+mi33hJDMulwterzdv58tZggNAY2MjIpEINbgVuFu3buH06dPSEyz9fj8uXLiQtI9YTX/33Xdx+vRpSvQM9Pb2gmEYmM3mvJ0z69lkKxEb3MbHx3N9KpKFsrIyafy5+Pd8n332WdJrpaWleYtNCxKJBLq6ujAyMpLX82Y9H1wOJZ7QQLJD88HVpVYO5LSKLnK73ejp6aHlklUktx+cKE+8TVWjgMtLglODG1mtOI6Dy+VCf3+/KufPS4IDcw1uiUSC5oyrRG4/OFGW0+mE2+1W7cmuebkHF3Ech6qqKoRCofx08hOios7OTsTj8byMWFtO3kpwYK4U8Xq9OHDgQD5PS0jeRSIRDA0Nqd6omdcSXNTW1pb0/4RoCcdx2LVrFwKBgGpVc1FeS3BRW1sbxsbGaGwz0SS177vnUyXBAaC/vx8ulwscx6kVwqpy5swZuFwutcPQvM7OThiNxoJZQly1BDcYDPB4PDStNE8mJycRi8XUDkPTCuW+ez7VEhyYWxzCaDSis7NTzTAIyZrY3+3z+QqqO1LVBAcAj8eDgYEBmpCSY+Xl5Wmtqkrk43keBw4cQEdHR0Hcd8+nSiv6QizLwul0wufzFdwHRMhKcvFMMaWoXoIDgNFoREdHB5xOJzW6kaLicrlQU1NTkMkNFEiCA3PLPLW0tMDpdILnebXDIWRFbW1tWL9+fUHPksz5fPB0WK1WcBwHp9Op2uB8QuTo7e1FPB6Hz+dTO5SUCqYEF9XW1qKyshKtra1qh6IpbW1tNERYIcFgEAMDAwWf3EABJjgAnDx5EjzPU/eZguLxOM3HV0A0GkV7ezsCgYDaochSkAkOAB0dHRgbG6PppaRgiL09IyMjBdXXnUpB3YMv1N/fD4fDAb1eD4vFonY4Ra28vJwaL7MQjUbR3NyMQCBQVOMJCqIfPBWO4+BwOOB2uynJiSrE5C7GcRoFXYIDc3PIA4EADhw4AJ7nc/4sJ0LmCwaDOHv2bNGV3KKCL8FFPM/D4XBg//790hrdhORSMBhET08PfD5fUSY3UEQJLnI6naisrMSxY8fUDoVoWG9vLwYGBhAIBIqmQW0pBduKvhyfz4d4PE6rwaSpra0NDodD7TCKQnd3N8bGxoqqtXw5RZfgAKRF7GguuXzxeJzG+cvQ1taG27dvF8UgFjmKMsGBuS+iurpaanwjJFvNzc0AkNeHA+Za0SY4MPdAPJvNBofDQaXTCjZv3gyGYdQOoyAlEglUVVWhvLxcc7d+RdfItpRwOCytppHPJzeS4heJRKRH+mrx2tFEggNzv8IHDhyAzWajFnYiS2dnJ4aGhtDf36/ZB3EUdRV9PoPBgJGREcTjcaqyk5TEJZbi8ThGRkY0m9yAhhIcAHQ6HTo6OlBXV4fdu3fTOm9kkVgshl27dsFms6Gjo6Pou8FWJGjUxMSEYDabBa/Xq3YoBeHYsWOC1WpVOwxVBQIBwWw2C+Pj42qHkjeaKsHnYxgGoVAIt2/fpmWgMDdpZ7V+BjzPo7W1FX19fRgZGYHJZFI7pLzRbIIDc1V2r9eL6upqVFVV0aOSVqFwOIyqqiqUlZUV7YSRbBT8bDIl1NfXw2w2w+Vyoa+vDx6PR9MNK0vZvn37qvo3cxyH5uZmsCyL/v7+1TsGQO17hHzz+XwCwzCCz+dTOxSSI/Qd/49m+sHTIf66x2Ix+Hy+1fvrrjGJRAJOp1N67t1qqrEsZ1UmuCgSicDpdMJut8Ptdmu/y0TDzpw5g56eHni9XloUZB5NN7KtxGw2Y2JiAmVlZdi6dSuCwaDaIZE0iY1ojx8/xsTEBCX3Aqu6BJ+PZVm4XC7wPK/J9d/EW5KRkRG1Q1FEJBKR1s73eDyaHEeuBErwBcLhMNrb2wFAU4nudDrBsixCoZDaoWRFXJc8kUjA4/Fo5vvJlVVdRV+KxWJBKBSC2+1Ge3s7du3aRf3nBSAajcLhcMDpdKKurg7Xrl2j5JaBSvAVaKVE7+7uRjweh8fjUTuUtLAsi9bWVsRiMbjd7oJ9imehogSXSSuJXixisRjOnj2LcDgMj8eD2tpatUMqSpTgaRITneM4NDQ0wG63U3+rQnieh9/vR09PDziOQ0tLCy2RnSVK8AxFo1H09PRgcHAQFosFNpuNSpkMRSIR6bO02+1oaGigVnGFUIIrwO/3Y2hoCMFgELW1tWhoaCi4GUs8z4Pn+YKZbMFxHPx+P7q6uqDX69HQ0IDa2loabKQwSnAFiRdtT08PeJ5HXV0d6uvrC6IK73K5wLKs6v3g4rO1g8Eg7HY7mpqaaKhwDlE3mYL0ej0aGxsxPj6OQCCAx48fY+vWrdi6dStaW1tVHSknluD5xrIsuru74XA4sGbNGnR1daG6uhr37t2D1+ul5M4xKsHzIBqNIhgMYmxsDMFgEFarFdXV1bBarXmryudzoEswGMTo6CiCwaD0wMiamhpYrVaqgucZJbgK5ic7y7KwWCyoqamBxWLJWYnm9/sRi8Vysu53NBpFOBzG6OgowuGw9O+xWq1UQquMElxlHMclJUcsFoPFYoHBYJAeVmAwGAqi3z0WiyEWiyEajeL27dtgWRbRaBQmkynpR4pK6cJBCV6AwuEwEokEYrEYJicnkUgkEA6HYTAYwDAMTCYT1q9fn9SVpNPpsu5aikQi0n06z/OIRCKYnJwEy7KIRCJgGAYMw6CyshImkwlGo7HgegtIMkrwIiImfTQaxV9//YVIJCJtExNyPvEHYSksy4Jl2aTXzGazVPrqdDps374dDMPAaDRSv3SRogTXMPEHYSlGoxFGozHPEZF8owQnRMOoH5wQDaMEJ0TDKMEJ0TBKcEI0jBKcEA2jBCdEwyjBCdEwSnBCNIwSnBANowQnRMMowQnRsP8HoLvfBrMUeMAAAAAASUVORK5CYII=)
A mass
slips along the wall of a semispherical surface of radius
. The velocity at the bottom of the surface is
![](data:image/png;base64,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)
physics-General
physics-
Three forces of magnitudes 6N, 6N and
N at a corner of a cube along three sides as shown in figure. Resultant of these forces is
![](data:image/png;base64,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)
Three forces of magnitudes 6N, 6N and
N at a corner of a cube along three sides as shown in figure. Resultant of these forces is
![](data:image/png;base64,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)
physics-General