General
✓✗A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest, the force on the particle at time t is
- \( \sqrt{\dfrac{mk}{2}}\,t^{-1/2} \)
- \( \dfrac{1}{2}\sqrt{mk}\,t^{-1/2} \)
- \( \sqrt{mk}\,t^{-1/2} \)
- \( \sqrt{2mk}\,t^{-1/2} \)
General
✓✗The work done by a constant force \( \vec{F} \) in a displacement \( \vec{d} \) is
- \( \vec F\times\vec d \)
- \( |\vec F|\,|\vec d| \) always
- \( \dfrac{|\vec F|}{|\vec d|} \)
- \( \vec F\cdot\vec d \)
General
✓✗A ball moving at 10 m s−1 strikes head-on a massive wall that is moving towards it at 2 m s−1. If the collision is elastic, the ball rebounds with speed
- 8 m s−1
- 14 m s−1
- 10 m s−1
- 12 m s−1
General
✓✗A body of mass m1 moving with speed u collides head-on and elastically with a body of mass m2 at rest and rebounds with speed u/3. The ratio m2/m1 is
- 3
- 2
- 4
- \( \dfrac12 \)
General
✓✗A 1 kg body on a 1 m string moves in a vertical circle with speed 4 m s−1 at the top. The tension at the top is (g = 10 m s−2)
- 10 N
- 26 N
- 6 N
- 16 N
General
✓✗A conservative force F = (4 − 2x) N acts along the x-axis. Taking U = 0 at x = 0, the potential energy at x = 3 m is
- −12 J
- 12 J
- −3 J
- 3 J
General
✓✗A ball falls on a floor and the time between its first and second bounces is 2 s, while that between the second and third bounces is 1.2 s. The coefficient of restitution is
- 0.6
- 0.8
- 0.36
- 0.4
General
✓✗A particle is projected at an angle of 45° with the horizontal with kinetic energy K. The kinetic energy at the highest point will be
- \( \dfrac{K}{\sqrt{2}} \)
- \( \dfrac{K}{2} \)
- K
- 2K
General
✓✗A 4 kg block on a rough table (μk = 0.25) is connected over a smooth pulley at the edge to a hanging 2 kg block. The system starts from rest. The speed after the blocks move 1.5 m is (g = 10 m s−2)
- \( \sqrt5 \) m s−1
- 3 m s−1
- \( \sqrt{10} \) m s−1
- 2 m s−1
General
✓✗The power delivered by a force varies with time as P = 6t (W). The work done from t = 0 to t = 2 s is
- 24 J
- 6 J
- 3 J
- 12 J
General
✓✗A stone of mass 0.2 kg is projected vertically up with 20 m s−1 and reaches 15 m. The work done by air resistance is (g = 10 m s−2)
- −30 J
- 10 J
- −10 J
- −40 J
General
✓✗A mass of 0.5 kg moving with a speed of 1.5 m s−1 on a horizontal smooth surface collides with a nearly weightless spring of force constant k = 50 N/m.
The maximum compression of the spring would be
The maximum compression of the spring would be
- 1.5 m
- 0.15 m
- 0.5 m
- 0.12 m
General
✓✗For what value of a are the vectors \( (2\hat i + a\hat j + \hat k) \) and \( (4\hat i - 2\hat j - 2\hat k) \) perpendicular?
- −3
- 3
- 1
- 2
General
✓✗A particle moves in a potential U(x) = x4 − 2x2. The number of equilibrium points is
- 1
- 4
- 3
- 2
General
✓✗A pump lifts 100 litres of water per minute from a well 20 m deep and delivers it at the surface with a speed of 10 m s−1. The power needed is about (g = 10 m s−2)
- 417 W
- 83 W
- 333 W
- 500 W