Work, Energy and Power · Question 6

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

A bead P sliding on a frictionless semi-circular string (ACB) and it is at point S at t = 0 and at this instant the horizontal component of its velocity is v. Another bead Q of the same mass as P is ejected from point A at t = 0 along the horizontal string AB, with the speed v, friction between the beads and the respective strings may be neglected in both cases. Let tP and tQ be the respective times taken by beads P and Q to reach the point B, then the relation between tP and tQ is [figure]

1. tP < tQ
2. tP = tQ
3. tP > 1.25tQ
4. tP > tQ

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is true but Statement II is false
2. Statement I is false but Statement II is true
3. Both Statement I and Statement II are false
4. Both Statement I and Statement II are true

Potential energy (V) versus distance (x) is given by the graph. Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low. [figure]

1. FBC > FAB > FDE > FCD
2. FBC > FCD > FDE > FAB
3. FCD > FAB > FBC > FDE
4. FCD > FDE > FAB > FBC

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by x(t) = t2 + t + m, where = 1 m/s2, = 1 m/s and = 1 m. The work done on the body during the time interval t = 2 s to t = 3 s, is J.

1. 42
2. 24
3. 49
4. 12

An object of mass 1000 g experiences a time dependent force F = (2t i + 3t2 j ) N. The power generated by the force at time t is:

1. (2t2 + 18t3 ) W
2. (3t3 + 5t5 ) W
3. (2t3 + 3t5 ) W
4. (2t2 + 3t3 ) W