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Q. No.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 |
89%
Level 1: 80%+
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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 |
82%
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 |
78%
Level 2: 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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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 |
92%
Level 1: 80%+
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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 |
85%
Level 1: 80%+
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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 |
86%
Level 1: 80%+
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Given below are two statements:
In the light of the above statements, choose the correct answer from the options given below:
| Statement I: | An object moves from position \(r_1\) to position \(r_2\) under a conservative force field \(\vec{F}\). The work done by the force is \(W=-\int_{r_1}^{r_2} \vec{F} \cdot d\overrightarrow{r}\). |
| Statement II: | Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. |
| 1. | Both Statement I and Statement II are True |
| 2. | Statement I is False but Statement II is True |
| 3. | Statement I is True but Statement II is False |
| 4. | Both Statement I and Statement II are False |
Subtopic: Concept of Work |
59%
Level 3: 35%-60%
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A small both \(A\) of mass \(m\) is attached to a massless rigid rod of length \(1~\text{m}\) pivoted at point \(P\) and kept at an angle of \(60^{\circ}\) with vertical as shown in figure. At distance of \(1~\text{m}\) below point \(P\), an identical bob \(B\) is kept at rest on a smooth horizontal surface that extends to a circular track of radius \(R\) as shown in figure. If bob \(B\) just manages to complete the circular path of radius \(R\) upto a point \(Q\) after being hit elastically by bob \(A\), then radius \(R\) is: (in m)
1. \(\dfrac{3}{5}\)
2. \(\dfrac{1}{5}\)
3. \(\dfrac{2+\sqrt{3}}{5}\)
4. \(\dfrac{2-\sqrt{3}}{5}\)
1. \(\dfrac{3}{5}\)
2. \(\dfrac{1}{5}\)
3. \(\dfrac{2+\sqrt{3}}{5}\)
4. \(\dfrac{2-\sqrt{3}}{5}\)
Subtopic: Conservation of Mechanical Energy |
80%
Level 1: 80%+
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Two blocks with masses \(100~\text{g}\) and \(200~\text{g}\) are attached to the ends of springs \(A\) and \(B\) as shown in figure. The energy stored in \(A\) is \(E\). The energy stored in \(B\), when spring constants \(k_A, k_B~\text{of}~A~\text{and}~B,\), respectively satisfy the relation \(4k_A = 3k_B\), is:
1. \(4E\)
2. \(2E\)
3. \(3E\)
4. \(\dfrac{4}{3} {E}\)
1. \(4E\)
2. \(2E\)
3. \(3E\)
4. \(\dfrac{4}{3} {E}\)
Subtopic: Elastic Potential Energy |
86%
Level 1: 80%+
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