Work, Energy and Power

A bead of mass 'm' slides without friction on the wall of a vertical circular hoop of radius 'R' as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is 'R'. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes 'R', would be (spring constant is 'k', g is acceleration due to gravity) [figure]

1. 2Rg + kR2m
2. 3Rg + kR2m
3. 2Rg + 4kR2m
4. 2 gR + kR2m

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R In the light of the above statements, choose the most appropriate answer from the options given below

1. A is false but R is true
2. Both A and R are true but R is NOT the correct explanation of A
3. A is true but R is false
4. Both A and R are true and R is the correct explanation of A

A body of mass 4 kg is placed on a plane at a point P having coordinates (3, 4) m. Under the action of force F = (2 i + 3 j) N, it moves to a new point Q having coordinates (6, 10) m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of :

1. 4 : 3
2. 13 : 6
3. 1 : 2
4. 6 : 13

A force F= + x2 acts on an object in the x-direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant =1 N then will be

1. 15 N/m2
2. 10 N/m2
3. 12 N/m2
4. 8 N/m2

A force f=x2y i+y2 j acts on a particle in a plane x+y=10. The work done by this force during a displacement from (0,0) to (4 m,2 m) is Joule (round off to the nearest integer)

A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity v0 at the point ' A ', the string becomes slack when the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is . [figure]

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

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is : [figure] (Take acceleration due to gravity as 10 m/s2)

1. 3- 22
2. 2+ 33
3. 2+ 23
4. 3+ 32

A ball of mass 100 g is projected with velocity 20 m/s at 60 with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

1. 20 J
2. 5 J
3. 15 J
4. zero

A force F=2 i+b j+ k is applied on a particle and it undergoes a displacement i-2 j- k. What will be the value of b, if work done on the particle is zero.

1. 13
2. 12
3. 0
4. 2