Work, Energy and Power

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

Which one of the following forces cannot be expressed in terms of potential energy?

1. Frictional force
2. Coulomb's force
3. Restoring force
4. Gravitational force

A block of mass 25 kg is pulled along a horizontal surface by a force at an angle 45 with the horizontal. The friction coefficient between the block and the surface is 0.25. The block travels at a uniform velocity. The work done by the applied force during a displacement of 5 m of the block is :

1. 490 J
2. 970 J
3. 735 J
4. 245 J

A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

1. S4, 3gS2
2. S2, 3gS2
3. S4, 3gS2
4. S2, 3gS2

Two cylindrical vessels of equal cross sectional area of 2 m2 contain water up to heights 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is 103 kg/m3 and g = 10 m/s2)

1. 1 105 J
2. 4 104 J
3. 8 104 J
4. 6 104 J

[figure] Consider two blocks A and B of masses m1 = 10 kg and m2 = 5 kg that are placed on a frictionless table. The block A moves with a constant speed v = 3 m/s towards the block B kept at rest. A spring with spring constant k = 3000 N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)

1. 0.3 m
2. 0.1 m
3. 0.4 m
4. 0.2 m