Two blocks A and B of mass m and 2m respectively are connected by a massless spring of spring constant k. This system lies over a smooth horizontal surface. At t = 0 the block A has velocity u towards right (as shown) while speed of block B is zero, and the length of spring is equal to its natural length at that instant.
| Column-I | Column-II |
| (A) The velocity of block A | (P) Can never be zero |
| (B) The velocity of block B | (Q) May be zero at a certain instant of time |
| (C) The kinetic energy of system of two blocks | (R) Is minimum at maximum compression of spring |
| (D) The potential energy of spring | (S) Is maximum at maximum extension of spring |
| (T) Will vary sinusoidal with time. |
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This system undergoes simple harmonic motion about the center of mass, which remains stationary. The center of mass velocity is constant: . The blocks oscillate relative to the center of mass.
(A) Velocity of A: Varies sinusoidally around u/3. It can be zero. (Q, T)
(B) Velocity of B: Varies sinusoidally around u/3. It can be zero. (Q, T)
(C) Kinetic Energy: Minimum when spring PE is maximum (at max compression/extension). (R)
(D) Potential Energy: Maximum at maximum compression AND extension. (S)
Final Answer: A → Q, T; B → Q, T; C → R; D → S