The minimum work done in pulling up a block of wood weighing \(2\) kN for a length of \(10\) m on a smooth plane inclined at an angle of \(15^\circ\) with the horizontal is (given: \(\mathrm{sin}15^\circ=0.2588)\):
1. \(4.36\) kJ
2. \(5.17\) kJ
3. \(8.91\) kJ
4. \(9.82\) kJ

Subtopic:  Work done by constant force |
 79%
From NCERT
PMT - 2003
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A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It slides down a smooth surface to the ground, then climbs up another hill of height 30 m and finally slides down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is: 

1. \(10 \mathrm{~m} / \mathrm{s} \) 2. \(10 \sqrt{30} \mathrm{~m} / \mathrm{s} \)
3. \(40 \mathrm{~m} / \mathrm{s} \) 4. \(20 \mathrm{~m} / \mathrm{s}\)
Subtopic:  Conservation of Mechanical Energy |
 61%
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A quarter horse-power motor runs at a speed of 600 rpm. Assuming 40% efficiency, the work done by the motor in one rotation will be: 

1. 7.46 J

2. 7400 J

3. 7.46 ergs

4. 74.6 J

Subtopic:  Power |
 54%
From NCERT
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Two equal masses, \(m_1\) and \(m_2,\) moving in the same straight line at velocities +3 m/s and –5 m/s respectively, collide elastically. Their velocities after the collision will be:

1. +4 m/s for both

2. –3 m/s and +5 m/s

3. –4 m/s and +4 m/s

4. –5 m/s and +3 m/s

Subtopic:  Collisions |
 81%
From NCERT
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A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on the table is:

1. \(MgL\)

2. \(MgL/3\)

3. \(MgL/9\)

4. \(MgL/18\)

Subtopic:  Gravitational Potential Energy |
 72%
From NCERT
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A particle of mass 'm' is moving in a horizontal circle of radius 'r' under a centripetal force equal to –K/r2, where K is a constant. The total energy of the particle will be:

1. K2r

2. K2r

3. Kr

4. Kr

Subtopic:  Potential Energy: Relation with Force |
 58%
From NCERT
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A force F=k(yi+xj) (where k is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force on the particle is:

1. 2ka2

2. 2ka2

3. −ka2

4. \(ka^2\)

Subtopic:  Work Done by Variable Force |
 56%
From NCERT
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A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then:

1. Lorry will come to rest in a shorter distance

2. Car will come to rest in a shorter distance

3. Both will come to rest in a same distance

4. None of the above

Subtopic:  Work Energy Theorem |
 64%
From NCERT
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The relationship between force and position is shown in the given figure (in a one-dimensional case). The work done by the force in displacing a body from \(x = 1\) cm to \(x = 5\) cm is:

1. \(20\) ergs
2. \(60\) ergs
3. \(70\) ergs
4. \(700\) ergs

Subtopic:  Work Done by Variable Force |
 83%
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The graph between the resistive force \(F\) acting on a body and the distance covered by the body is shown in the figure. The mass of the body is \(25\) kg and the initial velocity is \(2\) m/s. When the distance covered by the body is \(4\) m, its kinetic energy would be:

   
1. \(50\) J
2. \(40\) J
3. \(20\) J
4. \(10\) J

Subtopic:  Work Done by Variable Force |
 53%
From NCERT
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