# 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

Subtopic: Â Work Energy Theorem |
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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:

1. $$\sqrt{2gL}$$
2. $$\sqrt{2gL}$$ $$cos 60^\circ$$
3. $$\sqrt{2g(L-L~cos60^\circ)}$$
4. $$\sqrt{2gL}$$ $$sin 60^\circ$$

Subtopic: Â Gravitational Potential Energy |
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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
Subtopic: Â Elastic Potential Energy |
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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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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. $$\sqrt{\frac{k}{m}}\Big(\frac{x}{2}\Big)$$
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 $$\overrightarrow{v_1},~\overrightarrow{v_2}$$. Final velocities $$\overrightarrow{v_1},~\overrightarrow{v_2}$$ are in different directions. The angle between $$\overrightarrow{v_1}$$ and $$\overrightarrow{v_2}$$ is:
 1 $$\frac{\pi}{6}$$ 2 $$\frac{\pi}{3}$$ 3 $$\frac{\pi}{2}$$ 4 $$\frac{2\pi}{3}$$
Subtopic: Â 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
Subtopic: Â 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
Subtopic: Â Work Done by Variable Force |
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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. $$t\sqrt t$$
Subtopic: Â 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: Â Work done by constant force |
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