# Block A moves on a smooth surface and collides with block B at rest. The maximum energy stored in the spring will be:   1. $$\frac{1}{8} m v^2$$ 2. $$\frac{1}{4} \mathrm{~m} v^2$$ 3. $$\frac{1}{3} m v^2$$ 4. $$\frac{1}{2} m v^2$$

Subtopic:  Collisions |
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A particle of mass 'm' is projected at an angle '$\mathrm{\alpha \text{'}}$ with the horizontal, with an initial velocity 'u'. The work done by gravity during the time it reaches its highest point is:

1. ${u}^{2}{\mathrm{sin}}^{2}a$

2. $\frac{m{u}^{2}{\mathrm{cos}}^{2}\alpha }{2}$

3. $\frac{m{u}^{2}{\mathrm{sin}}^{2}\alpha }{2}$

4. $-\frac{m{u}^{2}{\mathrm{sin}}^{2}\alpha }{2}$

Subtopic:  Gravitational Potential Energy |
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A water pump rated 400 W has an efficiency of 75%. If it is employed to raise water to a height of 40 m, then the volume of water drawn in 10 min is:

 1 10.9 m3 2 0.45 m3 3 1.8 m3 4 0.25 m3
Subtopic:  Power |
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The position-time graph of a particle of mass 2 kg is shown in the figure. Total work done on the particle from t = 0 to t = 4s is:

 1 8 J 2 4 J 3 0 J 4 Can't be determined
Subtopic:  Work done by constant force |
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Five balls are placed one after another along a straight line as shown in the figure. Initially, all the balls are at rest. Then the second ball is projected with speed ${\mathrm{v}}_{0}$ towards the third ball. Mark the correct statement(s). (Assume all collisions to be head-on and elastic):

1. The total number of collisions in the process is 5.

2. The velocity of separation between the first and fifth ball after the last possible collision is ${\mathrm{v}}_{0.}$

3. Finally, three balls remain stationary.

4. All of the above are correct.

Subtopic:  Collisions |
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A particle moves with a velocity of $\left(5\stackrel{^}{\mathrm{i}}-3\stackrel{^}{\mathrm{j}}+6\stackrel{^}{\mathrm{k}}\right)$m/s under the influence of a constant force $\stackrel{\to }{F}=\left(10\stackrel{^}{\mathrm{i}}+10\stackrel{^}{\mathrm{j}}+20\stackrel{^}{\mathrm{k}}\right)$ N. The instantaneous power applied to the particle is:

 1 200 J/s 2 40 J/s 3 140 J/s 4 170 J/s
Subtopic:  Power |
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A body of mass 2 kg moving with a velocity of 3 m/s collides with a body of mass of 1 kg moving with a velocity of 4 m/s in the opposite direction. If the collision is head-on and completely inelastic, then the wrong statement is:

1. Both bodies move together with a velocity (2/3) m/s.

2. The momentum of the system is 2 kg-m/s throughout.

3. The momentum of the system is 10 kg-m/s.

4. The loss of KE for the system is (49/3) J.

Subtopic:  Collisions |
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The power supplied to a particle of mass 2 kg varies with time as $\mathrm{P}=\frac{3{\mathrm{t}}^{2}}{2}$ Watt, where t is in seconds. If the velocity of a particle at t = 0 is v = 0, then the velocity of the particle at t = 2 s will be:

 1 $$1 \mathrm{~m} / \mathrm{s}$$ 2 $$4 \mathrm{~m} / \mathrm{s}$$ 3 $$2 \mathrm{~m} / \mathrm{s}$$ 4 $$2 \sqrt{2} \mathrm{~m} / \mathrm{s}$$
Subtopic:  Power |
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The potential energy of a 1 kg particle free to move along the x-axis is given by:

The total mechanical energy of the particle is 2J. Then, the maximum speed (in ms-1) will be
1. $$3 \over \sqrt{2}$$
2. $$\sqrt{2}$$
3. $$1 \over \sqrt{2}$$
4. 2

Subtopic:  Conservation of Mechanical Energy |
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A smooth sphere of mass M, moving with velocity u, directly collides elastically with another sphere of mass m at rest. After the collision, their final velocities are V and v, respectively. The value of v is:

1. $$\frac{2 um}{m}$$

2. $$\frac{2 um}{M}$$

3. $$\frac{2 u}{1 + {m \over M}}$$

4. $$\frac{2 u}{1 + {M \over m}}$$

Subtopic:  Collisions |
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