Work, Energy and Power

A body of mass ‘m’ connected to a massless and unstretchable string goes in vertical circle of radius ‘R’ under gravity g. The other end of the string is fixed at the center of circle. If velocity at top of circular path is n gR, where, n 1, then ratio of kinetic energy of the body at bottom to that at top of the circle is :

1. n2+4n2
2. n+4n
3. n2n2+4
4. nn+4

As shown below, bob A of a pendulum having massless string of length 'R' is released from 60 to the vertical. It hits another bob B of half the mass that is at rest on a frictionless table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.) [figure]

1. 43 Rg
2. 13 Rg
3. Rg
4. 23 Rg

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., dmdt v. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

1. P v
2. P v
3. P2 v3
4. P2 v5

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 correct answer from the options given below:

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

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