Work, Energy and Power · Question 1

Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of length 10 m, as shown in the figure. Point mass A of mass m travelling horizontally with speed 10 ms-1 hits bob B elastically. The bob B rises h meter after the collision. Taking the acceleration due to gravity g = 10 ms-2 and neglecting the size of the bob, the value of h is: [figure]

1. 2.5
2. 8
3. 7
4. 5

A particle of mass M moves along a horizontal x axis from x = 0 to x = L. The coefficient of kinetic friction varies as a function of x as k(x) = 0 - x, where 0, are constants of appropriate dimensions, so that k(L) = 0. The total work done by the frictional force during the motion is n 0MgL, where g is the acceleration due to gravity. The value of n is:

1. 12
2. 3
3. 1
4. 13

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If FA and FB are the forces applied by the brakes on cars A and B respectively, then the ratio of FAFB is

1. 13
2. 12
3. 32
4. 23

A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity v0 as shown in figure. If the string gets slack at some point P making an angle from the horizontal, the ratio of the speed v of the bob at point P to its initial speed v0 is: [figure]

1. ( 2 + 3 ) 12
2. ( 2 + 3 ) 12
3. ( ) 12
4. ( 12 + 3 ) 12

At any instant of time t, the displacement of any particle is given by 2t - 1 (SI unit) under the influence of force of 5 N. The value of instantaneous power is (in SI unit):

1. 10
2. 5
3. 7
4. 6

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v1 while body B is at rest before collision. The velocity of the system after collision is v2. The ratio v1 : v2 is

1. 1 : 2
2. 2 : 1
3. 4 : 1
4. 1 : 4

An object moving along horizontal x-direction with kinetic energy 10 J is displaced through x = (3 i) m by the force F = (-2 i + 3 j) N. The kinetic energy of the object at the end of the displacement x is

1. 10 J
2. 16 J
3. 4 J
4. 6 J

An object falls from a height of 10 m above the ground. After striking the ground it loses 50\% of its kinetic energy. The height upto which the object can rebound from the ground is:

1. 7.5 m
2. 10 m
3. 2.5 m
4. 5 m

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, potential energy stored in it will be :

1. 4U
2. 8U
3. 16U
4. 2U

An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 ms-1. The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is : (g = 10 ms-2)

1. 23000
2. 20000
3. 34500
4. 23500