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Q. No.A mass of \(1~\text{kg}\) is kept on a inclined plane with \(30^\circ\) inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of \(4~\text{m/s}\). The work done by the frictional force in time \(2~\text{s}\) is: (in J) (Take \(g=10~\text{m/s}^2\))
1. \(20\)
2. \(25\)
3. \(30\)
4. \(10\)
Subtopic: Work done by constant force |
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Level 3: 35%-60%
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A particle of charge \(q\) and mass \(m\) is projected from origin with an initial velocity \(\vec{v}=\left(\dfrac{v_0}{\sqrt{2}} \hat{x}+\dfrac{v_0}{\sqrt{2}} \hat{y}\right)\). There exists a uniform magnetic field \(\vec{B}=B_0 \hat{z}\) and a space varying electric field \(\vec{E}=E_{{0}} {e}^{-\lambda x} \hat{x}\) within the region \(0 \leqslant x \leqslant L .\) After travelling a distance such that \(x\text-\)coordinate has changed from \(x=0\) to \(x=L,\) the changed in the kinetic energy is:
1. \(\dfrac{q E_0}{\lambda}\left[1-e^{-\lambda L}\right]\)
2. \(\left(\dfrac{v_0 q B_0}{2 \lambda}\right)\left[2-e^{-2 \lambda L}\right]\)
3. \(\dfrac{q E_0}{\lambda}\left[1+e^{-\lambda L}\right]\)
4. \(q\left(\dfrac{E_0+v_0 B_0}{\lambda}\right)\left[1-e^{-\lambda L / 2}\right]\)
1. \(\dfrac{q E_0}{\lambda}\left[1-e^{-\lambda L}\right]\)
2. \(\left(\dfrac{v_0 q B_0}{2 \lambda}\right)\left[2-e^{-2 \lambda L}\right]\)
3. \(\dfrac{q E_0}{\lambda}\left[1+e^{-\lambda L}\right]\)
4. \(q\left(\dfrac{E_0+v_0 B_0}{\lambda}\right)\left[1-e^{-\lambda L / 2}\right]\)
Subtopic: Work Energy Theorem |
Level 3: 35%-60%
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The rain drop of mass \(1~\text{g},\) starts with zero velocity from a height of \(1~\text{km}.\) It hits the ground with a speed of \(5~\text{m/s}.\) The work done by the unknown resistive force is: (in J) (take \(g = 10 ~\text{m/s}^2\))
1. \(-8.75\)
2. \(-8.35\)
3. \(-9.55\)
4. \(-9.98\)
1. \(-8.75\)
2. \(-8.35\)
3. \(-9.55\)
4. \(-9.98\)
Subtopic: Work Energy Theorem |
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Level 1: 80%+
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A smooth inclined plane ends in a vertical circular loop, as shown in figure. A small body is released from height \(h\) as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height \(h =\alpha{R}.\) The value of \(\alpha\) is:
1. \(2\)
2. \(4\)
3. \(3\)
4. \(6\)
1. \(2\)
2. \(4\)
3. \(3\)
4. \(6\)
Subtopic: Conservation of Mechanical Energy |
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Level 2: 60%+
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A \(1 ~\text{kg}\) block subjected to two simultaneous forces \((2 \hat{i}+3 \hat{j}+4 \hat{k}) \text{N}\) and \((3 \hat{i}-\hat{j}-2 \hat{k})\text{N}\) is moved a distance of \(25~\text{m}\) along \((3 \hat{{i}}-4 \hat{{j}})\) direction. The work done in this process is: (in J)
1. \(50\)
2. \(35\)
3. \(40\)
4. \(60\)
1. \(50\)
2. \(35\)
3. \(40\)
4. \(60\)
Subtopic: Work done by constant force |
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A body of mass \(2~\text{kg}\) begins to move under the influence of time dependent force \(\overrightarrow{{F}}=\left(2 {t} \hat{{i}}+6 {t}^2 \hat{{j}}\right)\text{N}\), where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\text{-axis}\) respectively. The power produced by the force at \(t=2~\text{s}\) is: (in W)
1. \(100\)
2. \(200\)
3. \(300\)
4. \(400\)
1. \(100\)
2. \(200\)
3. \(300\)
4. \(400\)
Subtopic: Power |
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A body of mass \(1~\text{kg}\) moves along a straight line with a velocity \(v =2x^{2}.\) The work done by the body during displacement from \(x=0\) to \(5~\text{m}\) is: (in J)
1. \(0\)
2. \(250\)
3. \(1250\)
4. \(1000\)
1. \(0\)
2. \(250\)
3. \(1250\)
4. \(1000\)
Subtopic: Work Energy Theorem |
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Three masses \(200~\text{kg}\), \(300~\text{kg}\) and \(400~\text{kg}\) are placed at the vertices of an equilateral triangle with sides \(20~\text{m}\). They are rearranged on the vertices of a bigger triangle of side \(25~\text{m}\) and with the same centre. The work done in this process: (in J)
(Gravitational constant \(G=6.7 \times 10^{-11} ~\text{N m}^2/ \text{kg}^2\))
1. \(9.86 \times 10^{-6} \)
2. \( 2.85 \times 10^{-7} \)
3. \(1.74 \times 10^{-7}\)
4. \(4.77 \times 10^{-7}\)
(Gravitational constant \(G=6.7 \times 10^{-11} ~\text{N m}^2/ \text{kg}^2\))
1. \(9.86 \times 10^{-6} \)
2. \( 2.85 \times 10^{-7} \)
3. \(1.74 \times 10^{-7}\)
4. \(4.77 \times 10^{-7}\)
Subtopic: Work done by constant force |
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A body of mass \(2~\text{kg}\) is moving along \(x\text-\)direction such that its displacement as function of time is given by \(x(t)=\alpha t^2+\beta t+\gamma m,\) where \(\alpha=1 ~\text{m/s}^2\), \(\beta=1~\text{m/s}\) and \(\gamma=1~\text{m}.\) The work done on the body during the time interval \(t= 2~\text{s and}~3~\text{s},\) is: (in J)
1. \(49\)
2. \(42\)
3. \(24\)
4. \(12\)
1. \(49\)
2. \(42\)
3. \(24\)
4. \(12\)
Subtopic: Work done by constant force |
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In a perfectly inelastic collision, two spheres made of the same material with masses \(15~\text{kg}\) and \(25~\text{kg}\), moving in opposite directions with speeds of \(10~\text{m/s}\) and \(30~\text{m/s}\), respectively, strike each other and stick together. The rise in temperature (in \(^{\circ}\text{C}\)), if all the heat produced during the collision is retained by these spheres, is:
(specific heat of sphere material \(31\) cal/kg.oC and \(1\) cal = \(4.2\) J)
1. \(1.75\)
2. \(1.44\)
3. \(1.15\)
4. \(1.95\)
(specific heat of sphere material \(31\) cal/kg.oC and \(1\) cal = \(4.2\) J)
1. \(1.75\)
2. \(1.44\)
3. \(1.15\)
4. \(1.95\)
Subtopic: Collisions |
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Level 2: 60%+
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