# A body of mass ($$4m$$) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass ($$m$$) move perpendicular to each other with equal speeds ($$u$$). The total kinetic energy generated due to explosion is: 1. $$mu^2$$ 2. $$1.5~mu^2$$ 3. $$2~mu^2$$ 4. $$3~mu^2$$

Subtopic:  Concept of Work |
61%
From NCERT
AIPMT - 2014
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A uniform force of $$(3 \hat{i} + \hat{j})$$ newton acts on a particle of mass $$2$$ kg. Hence the particle is displaced from position $$(2 \hat{i} + \hat{k})$$ meter to position $$(4 \hat{i} + 3 \hat{j} - \hat{k})$$ meter. The work done by the force on the particle is:

 1 $$6$$ J 2 $$13$$ J 3 $$15$$ J 4 $$9$$ J

Subtopic:  Concept of Work |
80%
From NCERT
AIPMT - 2013
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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $$1$$ kg moves with a speed of $$12$$ ms–1 and the second part of mass $$2$$ kg moves with $$8$$ ms–1 speed. If the third part flies off with $$4$$ ms–1 speed, then its mass is:
1. $$5$$ kg
2. $$7$$ kg
3. $$17$$ kg
4. $$3$$ kg
Subtopic:  Collisions |
70%
From NCERT
AIPMT - 2013
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The potential energy of a particle in a force field is $$U=$$$\frac{A}{{r}^{2}}-\frac{B}{r}$ where $$A$$ and $$B$$ are positive constants and $$r$$ is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

 1 $$\frac{B}{A}$$ 2 $$\frac{B}{2A}$$ 3 $$\frac{2A}{B}$$ 4 $$\frac{A}{B}$$

Subtopic:  Potential Energy: Relation with Force |
77%
From NCERT
AIPMT - 2012
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Two spheres $$A$$ and $$B$$ of masses $$m_1$$ and $$m_2$$, respectively, collide. $$A$$ is at rest initially and $$B$$ is moving with velocity $$v$$ along the $$x$$-axis. After the collision, $$B$$ has a velocity $$\frac{v}{2}$$ in a direction perpendicular to the original direction. The mass $$A$$ moves after collision in the direction:

 1 same as that of $$B$$. 2 opposite to that of $$B$$. 3 $$\theta = \text{tan}^{-1}\left(\frac{1}{2} \right)$$ to the positive $$x$$-axis. 4 $$\theta = \text{tan}^{-1}\left(\frac{-1}{2} \right )$$ to the positive $$x$$-axis.
Subtopic:  Collisions |
From NCERT
AIPMT - 2012
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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 |
66%
From NCERT
AIPMT - 2011
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Force $$F$$ on a particle moving in a straight line varies with distance $$d$$ as shown in the figure. The work done on the particle during its displacement of $$12$$ m is:

1. $$21$$ J
2. $$26$$ J
3. $$13$$ J
4. $$18$$ J

Subtopic:  Work Done by Variable Force |
72%
From NCERT
AIPMT - 2011
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A ball moving with velocity 2 ms-1 collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ms-1) after the collision will be:

1. 0, 1

2. 1, 1

3. 1, 0.5

4. 0, 2

Subtopic:  Collisions |
68%
From NCERT
AIPMT - 2010
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An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 ms-1. The mass per unit length of water in the pipe is $100$ $kg$ ${m}^{-1}.$What is the power of the engine?

1. 400 W

2. 200 W

3. 100 W

4. 800 W

Subtopic:  Power |
From NCERT
AIPMT - 2010
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A body of mass $$1$$ kg is thrown upwards with a velocity $$20$$ ms-1. It momentarily comes to rest after attaining a height of $$18$$ m. How much energy is lost due to air friction?
(Take $$g=10$$ ms-2)
1. $$20$$ J
2. $$30$$ J
3. $$40$$ J
4. $$10$$ J

Subtopic:  Work Energy Theorem |
87%
From NCERT
AIPMT - 2009
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