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 |
 69%
From NCERT
AIPMT - 2013
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The potential energy of a particle in a force field is \(U=\)Ar2-Br 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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