# 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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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 |
66%
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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 |
66%
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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 |
91%
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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 |
59%
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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 |
57%
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In the diagram shown, force F acts on the free end of the string. If the weight W moves up slowly by distance h, then work done on the weight by the string holding it will be: (Pulley and string are ideal)

1. Fh

2. 2Fh

3. $\frac{Fh}{2}$

4. 4Fh

Subtopic:  Work done by constant force |
67%
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The diagram represents a particle's potential energy curve in a field. The particle will be in equilibrium at which position(s):

1. $$B$$ and $$D$$
2. $$A$$ and $$C$$
3. $$A,B$$ and $$C$$
4. $$A,B,C$$ and $$D$$

Subtopic:  Potential Energy: Relation with Force |
66%
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A body of mass 'm' is released from the top of a fixed rough inclined plane as shown in the figure. If the frictional force has magnitude F, then the body will reach the bottom with a velocity: $\left(\mathrm{L}=\sqrt{2}\mathrm{h}\right)$

 1 $$\sqrt{2 g h}$$ 2 $$\sqrt{\frac{2 F h}{m}}$$ 3 $$\sqrt{2 g h+\frac{2 F h}{m}}$$ 4 $$\sqrt{2 g h-\frac{2 \sqrt{2} F h}{m}}$$
Subtopic:  Work Energy Theorem |
62%
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A body constrained to move along the $$\mathrm{z}$$-axis of a coordinate system is subjected to constant force given by $$\vec{F}=-\hat{i}+2 \hat{j}+3 \hat{k}$$ where $$\hat{i},\hat{j}$$ and $$\hat{k}$$ are unit vectors along the $$\mathrm{x}$$-axis, $$\mathrm{y}$$-axis and $$\mathrm{z}$$-axis of the system respectively. The work done by this force in moving the body a distance of $$4$$ m along the $$\mathrm{z}$$-axis will be:
1. $$15$$ J
2. $$14$$ J
3. $$13$$ J
4. $$12$$ J

Subtopic:  Concept of Work |
89%
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