Question

Two blocks of masses $m_1$ and $m_2$ are connected with a light spring and placed over a plank moving with an acceleration $a$ as shown in figure. The coefficient of friction between the blocks and plank is $\mu$. The spring will

• A. Neither compresses nor be stretched for $a\le \mu g$
• B. Be compressed if $a\le \mu g$
• C. Be stretched if $a>\mu g$
• D. Be in its natural length under all conditions.

Answer 1

The correct option is D Be in its natural length under all conditions.

For $a\le \mu g$, the blocks will remain stationary with respect to the surface of the plank, so the stretch $x=0$.
For $a\ge \mu g$, both the blocks will move with respect to the surface of the plank with an acceleration $(a-\mu g)$. However at any instant no relative motion between the blocks exists, so still they don't stretch the spring.
Hence, the correct answer is (D).