General
✓✗Which of the following is a non-conservative force?
- Gravitational force
- Spring force
- Electrostatic force
- Friction
General
✓✗A rubber ball is dropped from a height of 5 m on a plane. On bouncing it rises to 1.8 m. The fraction of its velocity that the ball loses on bouncing is (take g = 10 m s−2)
- \( \dfrac{3}{5} \)
- \( \dfrac{9}{25} \)
- \( \dfrac{16}{25} \)
- \( \dfrac{2}{5} \)
General
✓✗Statement I: In vertical circular motion on a string, the speed of the body is not constant.
Statement II: Gravity has a tangential component at most points of the circle.
Statement II: Gravity has a tangential component at most points of the circle.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗A block of mass m on a smooth floor is attached to two springs of constants k1 and k2 on opposite sides (both fixed to walls). It is displaced by x. The total potential energy stored is
- \( \dfrac12(k_1 - k_2)x^2 \)
- \( \dfrac12\dfrac{k_1k_2}{k_1 + k_2}x^2 \)
- \( (k_1 + k_2)x^2 \)
- \( \dfrac12(k_1 + k_2)x^2 \)
General
✓✗A moving block of mass m collides with another stationary block of mass 4m. The lighter block comes to rest after the collision. If the initial velocity of the lighter block is v, the coefficient of restitution e will be
- 0.4
- 0.25
- 0.8
- 0.5
General
✓✗The work done by a variable force F(x) is equal to
- F times the final x
- the area under the F-t graph
- the slope of the F-x graph
- the area under the F-x graph
General
✓✗Statement I: A particle can be in equilibrium at a point where its potential energy is not zero.
Statement II: A particle is in equilibrium wherever its potential energy is zero.
Statement II: A particle is in equilibrium wherever its potential energy is zero.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗A particle of mass m moving at v collides head-on with a particle of mass 2m at rest and sticks to it. The kinetic energy after the collision is
- \( \dfrac{1}{9}mv^2 \)
- \( \dfrac12mv^2 \)
- \( \dfrac13mv^2 \)
- \( \dfrac16mv^2 \)
General
✓✗The potential energy of a particle is U = 3x2 − 12x (in J, x in m). The equilibrium position is at
- x = 0
- x = 4 m
- x = 1 m
- x = 2 m
General
✓✗A bob of mass m on a string of length l is released from the horizontal position. When the string makes angle θ with the vertical, the tension is
- mg cosθ
- 3mg cosθ
- 2mg cosθ
- mg(3 cosθ − 2)
General
✓✗A small block is released from rest at the top of a smooth fixed sphere of radius R. It leaves the sphere at a height above the centre of
- R
- \( \dfrac{2R}{3} \)
- \( \dfrac{R}{3} \)
- \( \dfrac{R}{2} \)
General
✓✗A particle moves under a conservative force with total energy E. At a point where U(x) = E, the particle
- has kinetic energy E
- is momentarily at rest (a turning point)
- has maximum speed
- cannot reach that point
General
✓✗A block of mass 2 kg is pushed 5 m up a smooth incline of 30° at constant speed. The work done by gravity is (g = 10 m s−2)
- 100 J
- 50 J
- −100 J
- −50 J
General
✓✗300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. The work done against friction is (take g = 10 m s−2)
- 1000 J
- zero
- 100 J
- 200 J
General
✓✗A 10 g bullet moving at 500 m s−1 passes through a 1 kg block hanging from a string and emerges at 100 m s−1. The height to which the block rises is (g = 10 m s−2)
- 0.4 m
- 0.8 m
- 0.2 m
- 1.6 m