Two blocks connected by a spring rest on a smooth horizontal plane as shown in Fig. A constant force `F` start 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_1gtm_2`.
B. Blocks start performing SHM about centre of mass of the system, which moves rectilinearly with constant acceleration.
C. Blocks start performing oscillation about centre of mass of the system with incresing amplitude.
D. Acceleration of `m_2` 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 tenstion in the spring. Therefore at initial moment `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_1` increases from zero initial value.
The blocks start 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 block 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 contant therefore amplitude of oscillation also remains constant. So, option (c ) is also wrong.
Acceleration of `m_2` is maximum at the instant when the spring in its manimum 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 at time `t=T`, `T=2`, `3T` .. also, where T is the period of oscillation, hence option (d) is wrong.