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Q. No.A cylinder of weight \( W\) rests on two smooth inclined planes forming a symmetric \(\mathrm{V} \text-\)groove, as shown in the figure. Which of the following correctly represents the free-body diagram of the cylinder?
1.
2.
3.
4.
Subtopic: Tension & Normal Reaction |
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A person of mass \(60~\text{kg}\) is standing in an elevator. Column-I lists different motion conditions of the elevator and Column-II provides the corresponding normal force (i.e., the force exerted by the floor on the person). Match the entries in Column-I with the appropriate values in Column-II.
| Column-I | Column-II | ||
| (A) | Elevator moving at constant speed | (I) | Force on the floor by the person \(=600\) N |
| (B) | Elevator accelerating upward at \(3~\text{ms}^{-2}\) | (II) | Force on the floor by the person \(=780\) N |
| (C) | Elevator accelerating downward at \(3~\text{ms}^{-2}\) | (III) | Force on the floor by the person \(=420\) N |
| 1. | \(\mathrm{A\text-I,B\text-II,C\text-III}\) | 2. | \(\mathrm{A\text-II,B\text-I,C\text-III}\) |
| 3. | \(\mathrm{A\text-III,B\text-I,C\text-II}\) | 4. | \(\mathrm{A\text-III,B\text-II,C\text-I}\) |
Subtopic: Application of Laws |
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A conical pendulum of length \(1~\text{m}\) makes an angle \(\theta=45^\circ\) with respect to the \(z\text-\)axis and moves in a circle in the \(xy\) plane. The radius of the circle is \(0.4~\text{m}\) and its center is vertically below \(O.\) The speed of the pendulum, in its circular path, will be:
(take \({g}=10~\text{ms}^{-2})\)
1. \(0.4~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.2~\text{m/s}\)
4. \(4~\text{m/s}\)
(take \({g}=10~\text{ms}^{-2})\)
1. \(0.4~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.2~\text{m/s}\)
4. \(4~\text{m/s}\)
Subtopic: Uniform Circular Motion |
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A spring is subjected to two different forces separately. When a force of \(3 ~\text N\) is applied, the spring elongates by \(a\) units, and when a force of \(2 ~\text N\) is applied, the elongation is \(b\) units. What is the value of \((2a – 3b) \text{?}\)
1. \(5\)
2. \(0\)
3. \(7\)
4. \(9\)
1. \(5\)
2. \(0\)
3. \(7\)
4. \(9\)
Subtopic: Spring Force |
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What net force is required to keep a \(1.0~\text{kg}\) puck moving in a circle of radius \(0.5~\text m\) on a horizontal, frictionless surface at a speed of \(2.0~\text{m/s}?\)
| 1. | \(2.0~\text N\) | 2. | \(4.0~\text N\) |
| 3. | \(8.0~\text N\) | 4. | \(16~\text N\) |
Subtopic: Uniform Circular Motion |
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A tennis ball of mass \(m\) strikes a racquet and rebounds with the same speed \(v\) as before impact. The ball approaches and leaves the racquet, making an angle \(\theta\) with the normal to the racquet’s surface, as shown in the figure. What is the magnitude of the change in the momentum of the ball?
| 1. | \(0\) | 2. | \(mv\) |
| 3. | \(2mv\) | 4. | \(2mv \cos\theta\) |
Subtopic: Newton's Laws |
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Two \(1~\text{kg}\) blocks are connected by a light inextensible string and the system is suspended by a spring of stiffness \(1000~\text{N/m}.\) Take \(g=10~\text{m/s}^2.\)
The extension in the spring, in equilibrium, is:
The extension in the spring, in equilibrium, is:
| 1. | \(1~\text{cm}\) | 2. | \(2~\text{cm}\) |
| 3. | \(0.5~\text{cm}\) | 4. | \(\sqrt2~\text{cm}\) |
Subtopic: Spring Force |
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A light, rigid block is placed on a horizontal surface. A horizontal force \(F_2\) and a vertical force \(F_1\) are exerted on the block, so that it just stops moving due to friction. It is observed that \(F_1=4F_2.\) The coefficient of friction between the block and the surface is:
| 1. | \(1\) | 2. | \(\dfrac12\) |
| 3. | \(\dfrac14\) | 4. | \(2\) |
Subtopic: Friction |
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The rope and pulley are ideal and there is no friction anywhere except between the \(10~\text{kg}\)-block and the horizontal plane, where \(\mu\) (coefficient of friction)\(=0.2.\) Take \(g=10~\text{m/s}^2,\) if required.
What is the maximum mass \(m\) (shown) that can be suspended from the string so that the system does not move?
What is the maximum mass \(m\) (shown) that can be suspended from the string so that the system does not move?
| 1. | \(m=10~\text{kg}\) | 2. | \(m=2~\text{kg}\) |
| 3. | \(m=12~\text{kg}\) | 4. | \(m=8~\text{kg}\) |
Subtopic: Friction |
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Assume that the rope and pulley are ideal, and that the system is frictionless. For what value of \(m\) will the \(4~\text{kg}\) remain at rest?
1. \(4~\text{kg}\)
2. \(8~\text{kg}\)
3. \(2~\text{kg}\)
4. \(1~\text{kg}\)
1. \(4~\text{kg}\)
2. \(8~\text{kg}\)
3. \(2~\text{kg}\)
4. \(1~\text{kg}\)
Subtopic: Application of Laws |
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