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Q. No.A small mirror of mass \(m\) is suspended by a massless thread of length \(l.\) Then the small angle through which the thread will be deflected when a short pulse of laser of energy \(E\) falls normal on the mirror: (\(c=\)speed of light in vacuum and \(g=\)acceleration due to gravity)
1. \(\theta=\dfrac{E}{m c \sqrt{g l}}\)
2. \(\theta=\dfrac{3E}{4 m c \sqrt{g l}}\)
3. \(\theta=\dfrac{E}{2 m c \sqrt{g l}}\)
4. \(\theta=\dfrac{2E}{mc \sqrt{g l}} \)
Subtopic: Conservation of Mechanical Energy |
Level 3: 35%-60%
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A block of mass \(25~ \text{kg} \) is pulled along a horizontal surface by a force at an angle \(45^\circ\) with the horizontal. The friction coefficient between the block and the surface is \(0.25.\) The block travels at a uniform velocity. The work done by the applied force during a displacement of \(5 ~\text m\) of the block is:
1. \(970~\text{J}\)
2. \(245~\text{J}\)
3. \(735~\text{J}\)
4. \(490~\text{J}\)
1. \(970~\text{J}\)
2. \(245~\text{J}\)
3. \(735~\text{J}\)
4. \(490~\text{J}\)
Subtopic: Work done by constant force |
76%
Level 2: 60%+
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A block of mass \(2~\text{kg}\) is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is \(2~\text{m}\) and spring constant is \(200~\text{N/m.} \) The block is pushed such that the length of the spring becomes \(1~\text{m}\) and then released. At distance \({x ~\text m} (x<2) \) from the wall. the speed of the block will be:
1. \(10[1-(2-{x})]^{\frac{3}{2}} ~\text{m/s} \)
2. \(10\left[1-(2-x)^2\right]^{\frac{1}{2}}~\text{m/s}\)
3. \(10\left[1-(2-x)^2\right]~\text{m/s}\)
4. \(10\left[1-(2-x)^2\right]^2 ~\text{m/s} \)
1. \(10[1-(2-{x})]^{\frac{3}{2}} ~\text{m/s} \)
2. \(10\left[1-(2-x)^2\right]^{\frac{1}{2}}~\text{m/s}\)
3. \(10\left[1-(2-x)^2\right]~\text{m/s}\)
4. \(10\left[1-(2-x)^2\right]^2 ~\text{m/s} \)
Subtopic: Conservation of Mechanical Energy |
84%
Level 1: 80%+
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A block of mass \(1 ~\text{kg},\) moving along \(x\text-\)axis with speed \(v_i = 10 ~\text{m/s} \) enters a rough region ranging from \(x = 0.1 \text{ m} \) to \(x = 1.9~\text{ m.} \) The retarding force acting on the block in this range is \(F_r = -kx ~\text{N,} \) with \(k = 10 ~\text{N/m.} \) Then the final speed of the block as it crosses rough region is:
1. \(4 ~\text{m/s} \)
2. \(6 ~\text{m/s} \)
3. \(8 ~\text{m/s} \)
4. \(10 ~\text{m/s} \)
1. \(4 ~\text{m/s} \)
2. \(6 ~\text{m/s} \)
3. \(8 ~\text{m/s} \)
4. \(10 ~\text{m/s} \)
Subtopic: Work Energy Theorem |
80%
Level 1: 80%+
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Consider two blocks \(A\) and \(B \) of masses \(m_1= 10~\text{kg }\) and \(m_2= 5~\text{kg }\) that are placed on a frictionless table. The block \(A\) moves with a constant speed \(v=3 ~\text{m/s} \) towards the block \(B \) kept at rest. A spring with spring constant \(k=3000 \text{ N/m} ~\) is attached with the block \(B \) as shown in the figure. After the collision, suppose that the blocks \(A \) and \(B, \) along with the spring in constant compression state, move together, then the compression in the spring is: (Neglect the mass of the spring)
1. \(0.1~\text m \)
2. \(0.4~\text m\)
3. \(0.2~\text m\)
4. \(0.3~\text m\)
1. \(0.1~\text m \)
2. \(0.4~\text m\)
3. \(0.2~\text m\)
4. \(0.3~\text m\)
Subtopic: Collisions |
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Level 1: 80%+
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A particle is released from height \(S\) above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
1. \(\dfrac{S}{2}, \sqrt{\dfrac{3 g S}{2}} ~\)
2. \(\dfrac{S}{4}, \sqrt{\dfrac{3 g S}{2}} ~\)
3. \(\dfrac{S}{4}, \dfrac{3 g S}{2} ~\)
4. \(\dfrac{S}{2}, \dfrac{3 g S}{2} \)
1. \(\dfrac{S}{2}, \sqrt{\dfrac{3 g S}{2}} ~\)
2. \(\dfrac{S}{4}, \sqrt{\dfrac{3 g S}{2}} ~\)
3. \(\dfrac{S}{4}, \dfrac{3 g S}{2} ~\)
4. \(\dfrac{S}{2}, \dfrac{3 g S}{2} \)
Subtopic: Conservation of Mechanical Energy |
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Level 1: 80%+
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Which one of the following forces cannot be expressed in terms of potential energy?
| 1. | Coulomb's force | 2. | Restoring force |
| 3. | Gravitational force | 4. | Frictional force |
Subtopic: Concept of Work |
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Level 1: 80%+
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An object of mass \(1000~\text{g}\) experiences a time dependent force \(\overrightarrow{{F}}=\left(2 t \hat{\imath}+3 \mathrm{t}^2 \hat{\jmath}\right) \text{N}.\) The power generated by the force at time \(t\) is:
1. \(\left(2 t^2+3 t^3\right) \text W\)
2. \(\left(2 t^2+18 t^3\right)\text W\)
3. \(\left(2 t^3+3 t^5\right) \text W\)
4. \(\left(3 t^3+5 t^5\right) \text W\)
1. \(\left(2 t^2+3 t^3\right) \text W\)
2. \(\left(2 t^2+18 t^3\right)\text W\)
3. \(\left(2 t^3+3 t^5\right) \text W\)
4. \(\left(3 t^3+5 t^5\right) \text W\)
Subtopic: Power |
91%
Level 1: 80%+
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A body of mass \(4 ~\text{kg}\) is placed on a plane at a point \(P\) having coordinate \((3,4)~\text m.\) Under the action of \(\vec{F}=(2 \hat{i}+3 \hat{j})~\text{N},\) it moves to a new point \(Q\) having coordinates \((6,10)~\text m\) in \(4 ~\text{s}.\) The average power and instantaneous power at the end of \(4 ~\text{s}\) are in the ratio of:
1. \(4 :3\)
2. \(6 :13\)
3. \(13 :6\)
4. \(1 :2\)
1. \(4 :3\)
2. \(6 :13\)
3. \(13 :6\)
4. \(1 :2\)
Subtopic: Power |
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Level 2: 60%+
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Given below are two statements:
Choose the most appropriate answer from the options given below:
| Assertion (A): | In a central force field, the work done is independent of the path chosen. |
| Reason (R): | Every force encountered in mechanics does not have an associated potential energy. |
Choose the most appropriate answer from the options given below:
| 1. | Both (A) and (R) are true, but (R) is not the correct explanation of (A) |
| 2. | (A) is false, but (R) is true |
| 3. | Both (A) and (R) are true, and (R) is the correct explanation of (A) |
| 4. | (A) is true, but (R) is false |
Subtopic: Concept of Work |
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Level 2: 60%+
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