Work, Energy and Power · Question 1

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height h as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height h= R. The value of is . [figure]

1. 2
2. 4
3. 3
4. 6

A body of mass 1 kg moves along a straight line with a velocity v=2x2. The work done by the body during displacement from x=0 to 5 m is J.

1. 0
2. 250
3. 1250
4. 1000

A mass of 1 kg is kept on an inclined plane with 30 inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of 4 m/s. The work done by the frictional force in time 2 s is J. (Take g=10 m/s2)

1. 20
2. 25
3. 30
4. 10

A 1 kg block subjected to two simultaneous forces (2 i+3 j+4 k ) N and (3 i- j-2 k ) N is moved a distance of 25 m along (3 i-4 j ) direction. The work done in this process is J.

A body of mass 2 kg begins to move under the influence of time dependent force F= (2t i+6t2 j ) N, where i and j are unit vectors along x and y-axis respectively. The power produced by the force at t=2 s is W.

A spherical ball of mass 2 kg falls from a height of 10 m and is brought to rest after penetrating 10 cm into sand. The average force exerted by sand on the ball is N. (Take g=10 m/s2)

1. 1980
2. 2020
3. 2000
4. 1000

In case of vertical circular motion of a particle by a thread of length r, if the tension in the thread is zero at an angle 30 shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration) [figure]

1. 72gr
2. 4gr
3. 52gr
4. 5gr

In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg, moving in opposite directions with speeds of 10 m/s and 30 m/s, respectively, strike each other and stick together. The rise in temperature (in ), if all the heat produced during the collision is retained by these spheres, is : (specific heat of sphere material 31 cal/(kg C) and 1 cal = 4.2 J)

1. 1.75
2. 1.44
3. 1.95
4. 1.15

A small bob A of mass m is attached to a massless rigid rod of length 1 m pivoted at point P and kept at an angle of 60 with vertical as shown in figure. At distance of 1 m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by bob A, then radius R is m. [figure]

1. 15
2. 2 - 35
3. 35
4. 2 + 35

Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants kA, kB of A and B, respectively satisfy the relation 4kA = 3kB, is : [figure]

1. 4E
2. 2E
3. 43E
4. 3E