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Q. No.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 |
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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 |
 73%
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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. \(5\) J
2. \(10 \) J
3. \(2.5 \) J
4. \(1.25\) J
where \(x\) is in \(\text{m}\) and \(\theta\) is in radians. The work done by this force until the force becomes vertical is:
1. \(5\) J
2. \(10 \) J
3. \(2.5 \) J
4. \(1.25\) J
Subtopic: Â Work Done by Variable Force |
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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 |
 63%
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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 |
 50%
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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%
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A particle of mass \(4M\) at rest splits into two particles of mass \(M\) and \(3M.\) The ratio of the kinetic energies of mass \(M\) and \(3M\) would be:
1. \(3:1\)
2. \(1:4\)
3. \(1:1\)
4. \(1:3\)
1. \(3:1\)
2. \(1:4\)
3. \(1:1\)
4. \(1:3\)
Subtopic: Â Collisions |
 66%
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A force of \(100~\text N\) acts on a block, always acting opposite to its velocity. The block moves from \(x=4~\text m\) to \(x=10~\text m\) and then to \(x=6~\text {m.}\) The work done by the force is:
1. \(200~\text J\)
2. \(-200~\text J\)
3. \(1000~\text J\)
4. \(-1000~\text J\)
1. \(200~\text J\)
2. \(-200~\text J\)
3. \(1000~\text J\)
4. \(-1000~\text J\)
Subtopic: Â Work done by constant force |
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The work done by a force \(F=2x^2\) (newton) in a displacement from \(x=0\) (origin) to \(x=3\) m is:
1. \(54\) J
2. \(27\) J
3. \(18\) J
4. \(9\) J
1. \(54\) J
2. \(27\) J
3. \(18\) J
4. \(9\) J
Subtopic: Â Work Done by Variable Force |
 83%
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A gravitational field is present in a region, and a mass is shifted from \(A\) to \(B\) through different paths as shown. If \(W_1\), \(W_2\) and \(W_3\) represent the work done by the gravitational force along their respective paths, then:
| 1. | \(W_1=W_2=W_3\) | 2. | \(W_1>W_2>W_3\) |
| 3. | \(W_1>W_3>W_2\) | 4. | \(W_1<W_2<W_3\) |
Subtopic: Â Gravitational Potential Energy |
 87%
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