# 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 $$t=4$$ s 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 $$\left(5\hat{i}-3\hat{j}+6\hat{k}\right)\text{m/s}$$ under the influence of a constant force $$\vec F = \left(10\hat{i}+10\hat j +20\hat k\right) \text{N}$$. The instantaneous power applied to the particle is:
 1 $$200~\text{J/s}$$ 2 $$40~\text{J/s}$$ 3 $$140~\text{J/s}$$ 4 $$170~\text{J/s}$$
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 |
66%
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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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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 water pump rated $$400~\text{W}$$ has an efficiency of $$75\%$$. If it is employed to raise water to a height of $$40~\text{m}$$, then the volume of water drawn in $$10~\text{min}$$ is:
1. $$10.9~\text{m}^{3}$$
2. $$0.45~\text{m}^{3}$$
3. $$1.8~\text{m}^{3}$$
4. $$0.25~\text{m}^{3}$$
Subtopic:  Power |
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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. $$Fh/2$$
4. $$4Fh$$

Subtopic:  Work done by constant force |
68%
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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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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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