Work, Energy and Power

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