Two inclined frictionless tracks, one gradual and the other steep meet at \(A\) from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

Which of the following statement is correct?

        

1. Both stones reach the bottom at the same time but not at the same speed.
2. Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.
3. Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
4. Both stones reach the bottom at different times and at different speeds.

Subtopic:  Gravitational Potential Energy |
 62%
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A body of mass \(0.5\) kg travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\mathrm{m^{-1/2}s^{-1}}\). The work done by the net force during its displacement from \(x=0\) m to \(x=2\) m is:
1. \(15\) J
2. \(50\) J
3. \(10\) J
4. \(100\) J

Subtopic:  Work Done by Variable Force |
 66%
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During an inelastic collision between two bodies, which of the following quantities always remain conserved?

1. total kinetic energy         
2. total mechanical energy
3. total linear momentum   
4. speed of each body
Subtopic:  Collisions |
 79%
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A bicyclist comes to a skidding stop in \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:

1. \(+2000\) J 2. \(-200\) J
3. zero 4. \(-20000\) J
Subtopic:  Work done by constant force |
 58%
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Which of the diagrams shown in the figure most closely shows the variation in kinetic energy of the earth as it moves once around the sun in its elliptical orbit?

1. 2.
3. 4.
Subtopic:  Conservation of Mechanical Energy |
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The angle between \(\mathrm{A}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(\mathrm{B}=\hat{\mathbf{i}}-\hat{\mathbf{j}}\) is:
1. \(45^{\circ} \)
2. \(90^{\circ} \)
3. \(-45^{\circ} \)
4. \(180^{\circ}\)
Subtopic:  Scalar Product |
 78%
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A ball is dropped from a height of \(5\) m. If it rebounds up to a height of \(1.8\) m, then the ratio of velocities of the ball after and before the rebound will be:
1. 35

2. 25

3. 15

4. 45 

Subtopic:  Conservation of Mechanical Energy |
 75%
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AIPMT - 1998
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In a ballistics demonstration, a police officer fires a bullet of mass \(50.0\) g with speed \(200\) m/s on soft plywood of thickness \(2.00\) cm. The bullet emerges with only \(\text{10%}\) of its initial kinetic energy. The emergent speed of the bullet is:

1. \(0\) 2. \(53.2\) m/s
3. \(63.2\) m/s 4. \(6.32\) m/s
Subtopic:  Work Energy Theorem |
 66%
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An elevator can carry a maximum load of \(1800\) kg (elevator + passengers) is moving up with a constant speed of \(2\) m/s. The frictional force opposing the motion is \(4000\) N. The minimum power delivered by the motor to the elevator is:
1. \(59000\) W
2. \(44000\) W
3. \(11000\) W
4. \(22000\) W

Subtopic:  Power |
 73%
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The work done by all the forces (external and internal) on a system equals the change in:

1. total energy 2. kinetic energy
3. potential energy 4. none of these
Subtopic:  Work Energy Theorem |
 73%
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