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Q. No.A block of \(1\) kg is released from the top of a smooth curve \(\mathrm{AB},\) and then it encounters a rough surface \(\mathrm{BC},\) coming to rest at \(\mathrm{C}.\) The work done by friction is:
(take \(g=10\) m/s2)
1.
\(25\) J
2.
\(50\) J
3.
\(-25\) J
4.
\(-50\) J
(take \(g=10\) m/s2)
Subtopic: Â Work Energy Theorem |
 72%
Level 2: 60%+
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The minimum speed that a simple pendulum's bob should be given so that it rises to a level where its string makes \(60^\circ\) with the vertical is:
2. \(\sqrt{2gL}\) \(\text{cos} 60^\circ\)
3. \(\sqrt{2g(L-L~\text{cos}60^\circ)}\)
4. \(\sqrt{2gL}\) \(\text{sin} 60^\circ\)
Subtopic: Â Gravitational Potential Energy |
 83%
Level 1: 80%+
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A block is suspended from a spring and causes an extension of \(2\) cm. It is now imparted a kinetic energy \(E\) so that the block rises up by exactly \(2\) cm. If the block were to be given the same kinetic energy upward, without being attached to a spring, it would rise up by:
1. \(1\) cm
2. \(2\) cm
3. \(4\) cm
4. \(8\) cm
1. \(1\) cm
2. \(2\) cm
3. \(4\) cm
4. \(8\) cm
Subtopic: Â Elastic Potential Energy |
Level 3: 35%-60%
Hints
The work done by all the forces (external and internal) on a system equals the change in:
1. total energy
2. kinetic energy
3. potential energy
4. none of these
Subtopic: Â Work Energy Theorem |
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Level 2: 60%+
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A block of mass \(m\) moving with a speed \(v\) meets an unextended spring fixed at one end, and having a spring constant \(k.\) During maximum compression, the mid-point of the spring undergoes a rightward displacement \(x\). Then, \(v=\)
| 1. | \(\sqrt{\dfrac{k}{m}}x\) | 2. | \(\sqrt{\dfrac{m}{k}}x\) |
| 3. | \(\sqrt{\dfrac{k}{m}}(2x)\) | 4. | \(\sqrt{\dfrac{k}{m}}\left(\dfrac{x}{2}\right)\) |
Subtopic: Â Work Done by Variable Force |
Level 3: 35%-60%
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A particle undergoes an elastic collision with an identical particle at rest. After the collision, the two particles move with velocities \(\vec{v_1},~\vec{v_2}.\) Final velocities \(\vec{v_1},~\vec{v_2}\) are in different directions. The angle between \(\vec{v_1}\) and \(\vec{v_2}\) is:
1. \(\dfrac{\pi}{6}\)
2. \(\dfrac{\pi}{3}\)
3. \(\dfrac{\pi}{2}\)
4. \(\dfrac{2\pi}{3}\)
1. \(\dfrac{\pi}{6}\)
2. \(\dfrac{\pi}{3}\)
3. \(\dfrac{\pi}{2}\)
4. \(\dfrac{2\pi}{3}\)
Subtopic: Â Collisions |
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Level 2: 60%+
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A block is moved along a horizontal plane by means of a force of constant magnitude of \(5\) N, but acting at an angle \(\theta\) which is proportional to the displacement (\(x\)): \(\theta=\dfrac{1}{2} x, \) where \(x\) is in \(\text{m}\) and \(\theta\) is in radians. The work done by this force until the force becomes vertical is:
1. \(5\text{ J}\)
2. \(10 \text{ J}\)
3. \(2.5\text{ J}\)
4. \(1.25\text{ J}\)
1. \(5\text{ J}\)
2. \(10 \text{ J}\)
3. \(2.5\text{ J}\)
4. \(1.25\text{ J}\)
Subtopic: Â Work Done by Variable Force |
Level 3: 35%-60%
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A horizontal force \(F\) acts on a \(2~\text{kg}\) block placed on a smooth horizontal plane. It varies with time \(t\) as shown in the figure. The block is initially at rest.
The work done by the force until \(t=2~\text s,\) equals:
1. \(6.25 ~\text J\)
2. \(4.5 ~\text J\)
3. \(2.25 ~\text J\)
4. \(1.5~\text J\)
The work done by the force until \(t=2~\text s,\) equals:
1. \(6.25 ~\text J\)
2. \(4.5 ~\text J\)
3. \(2.25 ~\text J\)
4. \(1.5~\text J\)
Subtopic: Â Work Done by Variable Force |
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Level 2: 60%+
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A car is driven by an engine that delivers constant power (except possibly at the initial instant). If it starts from rest, its displacement varies with time \((t)\) as:
1. \(t\)
2. \(\sqrt t \)
3. \(\dfrac{1}{\sqrt t}\)
4. \(t\sqrt t \)
1. \(t\)
2. \(\sqrt t \)
3. \(\dfrac{1}{\sqrt t}\)
4. \(t\sqrt t \)
Subtopic: Â Power |
 54%
Level 3: 35%-60%
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The work done by gravity on a projectile of mass \(m\) fired with a speed \(u\) at an angle \(\theta\) to the horizontal, until the time of impact is:
| 1. | zero | 2. | \(-\dfrac12mu^2\cos^2\theta\) |
| 3. | \(-\dfrac12mu^2\sin^2\theta\) | 4. | \(-\dfrac12mu^2\) |
Subtopic: Â Work done by constant force |
 61%
Level 2: 60%+
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