# 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 |
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The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

1. 2.5 m/s

2. 3.9 m/s

3. 4.7 m/s

4. 5.3 m/s

Subtopic:  Work Energy Theorem |
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A body of mass 0.5 kg travels in a straight line with velocity where . What is the work done by the net force during its displacement from x = 0 to x = 2 m?

1. 50 J

2. 45 J

3. 68 J

4. 90 J

Subtopic:  Work Energy Theorem |
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A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down at a uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?

1.  8.82 J

2.  7.65 J

3.  7.01 J

4.  7.98 J

Subtopic:  Gravitational Potential Energy |
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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 |
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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 |
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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 |
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The potential energy of a system increases if work is done:

1. by the system against a conservative force.

2. by the system against a non-conservative force.

3. upon the system by a conservative force.

4. upon the system by a non-conservative force.

Subtopic:  Potential Energy: Relation with Force |
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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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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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