# 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 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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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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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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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 |
60%
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The potential energy of a particle varies with distance r as shown in the graph. The force acting on the particle is equal to zero at:

 1 P 2 S 3 Both Q and R 4 Both P and S
Subtopic:  Potential Energy: Relation with Force |
88%
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A block of mass m is placed in an elevator moving down with an acceleration $\frac{\mathrm{g}}{3}$. The work done by the normal reaction on the block as the elevator moves down through a height h is:

1.  $\frac{-2\mathrm{mgh}}{3}$

2.  $\frac{-\mathrm{mgh}}{3}$

3.  $\frac{2\mathrm{mgh}}{3}$

4.  $\frac{\mathrm{mgh}}{3}$

Subtopic:  Work done by constant force |
66%
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A particle is moving such that the potential energy U varies with position in metre as U (x) = ($4{\mathrm{x}}^{2}$ - 2x + 50) J. The particle will be in equilibrium at:
1. x = 25 cm
2. x = 2.5 cm
3. x = 25 m
4. x = 2.5 m

Subtopic:  Potential Energy: Relation with Force |
78%
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