# A body constrained to move along the z-axis of a coordinate system is subjected to constant force given by $\stackrel{\to }{F}=-\stackrel{^}{i}+2\stackrel{^}{j}+3\stackrel{^}{k}$ where $\stackrel{^}{i}$, $\stackrel{^}{j}$ and $\stackrel{^}{k}$ are unit vectors along x-axis, y-axis and z-axis of the system respectively. The work done by this force in moving the body a distance of 4 m along the z-axis will be:

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. $\sqrt{2gh}$

2. $\sqrt{\frac{2Fh}{m}}$

3. $\sqrt{2gh+\frac{2Fh}{m}}$

4. $\sqrt{2gh-\frac{2\sqrt{2}Fh}{m}}$

Subtopic:  Work Energy Theorem |
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The given diagram represents the potential energy curve of a particle 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 m/s

2. 4 m/s

3. 2 m/s

4. $2\sqrt{2}$ m/s

Subtopic:  Power |
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