# 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 |
67%
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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An engine pumps water continuously through a hose. Water leaves the hose with a velocity $$v$$ and $$m$$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
1. $$\frac{1}{2}mv^3$$
2. $$mv^3$$
3. $$\frac{1}{2}mv^2$$
4. $$\frac{1}{2}m^2v^2$$

Subtopic:  Power |
78%
From NCERT
AIPMT - 2009
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A block of mass $$M$$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant value of $$k$$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:
1. $$Mg/k$$
2. $$2Mg/k$$
3. $$4Mg/k$$
4. $$Mg/2k$$
Subtopic:  Elastic Potential Energy |
69%
From NCERT
AIPMT - 2009
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