Two blocks connected by a spring rest on a smooth ITIM horizontal plane as shown in figure. A constant force F starts acting on block `m_(2)` as shown in the figure. Which of the following statements are not correct?

Options

A. Length of the spring increases continuously if `m_(1) gt m_(2)`
B. Blocks start performing SHM about centre of mass of the system, which moves rectilinearly with constant acceleration.
C. Blocks start performing oscillations about centre of mass of the system with increasing amplitude.
D. Acceleration of my is maximum at initial moment of time only.

Answer

A, C, D

Explanation

The only external horizontal force acting on the system of the two blocks and the spring is F. Therefore, acceleration of the centre of mass of the system is equal to
`F/(m_(1) + m_(2))`
Hence, centre of mass of the system moves with a constant acceleration. Initially, there is no tension in the spring, therefore `m_(2)` has an acceleration `F//m_(2)` and it starts to move to the right. Due to its motion, the spring elongates and a tension is developed. Therefore, acceleration of `m_(2)` decreases while that of m, increases from initial value zero. The blocks starts to perform SHM about their centre of mass and the centre of mass moves with the acceleration calculated above. Hence, option (b) is correct. Since the blocks perform SHM about centre of mass, therefore the length of the spring varies periodically. Hence, option (a) is wrong. Since magnitude of the force F remains constant, therefore amplitude of oscillations also remains constant. So, option (C) is also wrong. Acceleration of my is maximum at the instant when the spring is in its minimum possible length, which is equal to its natural length. Hence, at initial moments, acceleration of `m_(2)` is maximum possible.
The spring is in its natural length, not only at initial moment but also at time t= T, 27, 37, ...... where T is the period of oscillation. Hence, option (d) is also wrong