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Q. No.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
Subtopic: Elastic Potential Energy |
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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. \(\sqrt{\frac{k}{m}}x\)
2. \(\sqrt{\frac{m}{k}}x\)
3. \(\sqrt{\frac{k}{m}}(2x)\)
4. \(\sqrt{\frac{k}{m}}\Big(\frac{x}{2}\Big)\)
1. \(\sqrt{\frac{k}{m}}x\)
2. \(\sqrt{\frac{m}{k}}x\)
3. \(\sqrt{\frac{k}{m}}(2x)\)
4. \(\sqrt{\frac{k}{m}}\Big(\frac{x}{2}\Big)\)
Subtopic: 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 \(\overrightarrow{v_1},~\overrightarrow{v_2}\). Final velocities \(\overrightarrow{v_1},~\overrightarrow{v_2}\) are in different directions.
The angle between \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\) is:
The angle between \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\) is:
| 1. | \(\dfrac{\pi}{6}\) | 2. | \(\dfrac{\pi}{3}\) |
| 3. | \(\dfrac{\pi}{2}\) | 4. | \(\dfrac{2\pi}{3}\) |
Subtopic: Collisions |
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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 (\(x\)): \(\theta=\frac{1}{2} x,\)
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: Work Done by Variable Force |
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A horizontal force \(F\) acts on a \(2\) 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 \(t=2\) s, equals:
1. \(6.25 \) J
2. \(4.5 \) J
3. \(2.25 \) J
4. \(1.5\) J
The work done by the force until \(t=2\) s, equals:
1. \(6.25 \) J
2. \(4.5 \) J
3. \(2.25 \) J
4. \(1.5\) J
Subtopic: Work Done by Variable Force |
62%
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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. \(\frac{1}{\sqrt t}\)
4. \(t\sqrt t\)
1. \(t\)
2. \(\sqrt t\)
3. \(\frac{1}{\sqrt t}\)
4. \(t\sqrt t\)
Subtopic: Power |
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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. | \(-\frac12mu^2cos^2\theta\) |
| 3. | \(-\frac12mu^2sin^2\theta\) | 4. | \(-\frac12mu^2\) |
Subtopic: Work done by constant force |
60%
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A particle of mass \(4M\) kg 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: Collisions |
63%
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A force of \(100\) N acts on a block, always acting opposite to its velocity. The block moves from \(x=4\) m to \(x=10\) m and then to \(x=6\) m. The work done by the force is:
1. \(200\) J
2. \(-200\) J
3. \(1000\) J
4. \(-1000\) J
1. \(200\) J
2. \(-200\) J
3. \(1000\) J
4. \(-1000\) J
Subtopic: 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: Work Done by Variable Force |
83%
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