Two block of masses `m1` and `m2` are connected with a massless unstretched spring and placed over a plank moving with an acceleration `'a'` as shown in figure. The coefficient of friction between the blocks and platform is `mu`

Options

A. spring will be stretched if `agtmug`
B. spring will be compressed if `alemug`
C. spring will neither be compressed nor be stertched for `alemug`
D. spring will be in its natural length under all conditions

Answer

D

Explanation

Let the value of a be increased from zero. As long as `alemug`, there shall be no relative motion between `m_1` or `m_2` and platform, that is, `m_1` and `m_2` shall move with accelration a.
As `agtmug` the acceleration of `m_1` and `m_2` shall become `mug` each. Hence at all instants the velocity of `m_1` and `m_2` shall be same The spring shall always remaing in nature length.