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 `a gt mu g`.
B. spring will be compressed if `a le mu g `
C. spring will neither be compressed nor be stretched for `a le mu g` only
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 `a le mu g `, there shall be no relative motion between `m_(1)` or `m_(2)` and platform that is `m_(1)` and `m_(2)` shall move with acceleration a .
As `a gt mu g`, the acceleration of `m_(1)` and `m_(2)` shall be same .
`therefore` The spring shall always remain in natural length .