Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on the mass B as shown in the figure. If the mass A starts moving away from mass B with acceleration 'a', then the acceleration of mass B will be :

Solution

Physics sir · 4 steps

Look at A first: the spring is the only thing pulling it, so the spring force must be Ma.

1. Free body of A. The only horizontal force on A is the spring force. Newton's second law for A gives the spring force as kx = Ma. Force F pulls B to the left, so the spring stretches and pulls A towards the left as well.
2. Free body of B. The stretched spring pulls B back towards A, to the right, with the same force Ma. Force F pulls B to the left. The net force on B is F - Ma towards the left.

   M a_B = F - Ma ⇒ a_B = (F - Ma)/M

3. Quick check. Treat A, B and the spring as one system. The spring forces are internal, so F = M a_B + M a, which gives the same a_B.
4. So. The acceleration of B is (F - Ma)/M, in the direction of F. That is option (d).

The idea to keep. With a spring between two blocks, start with the block that feels only the spring. Its ma tells you the spring force. Then put that force, reversed, on the other block.

Answer from the NTA final answer key. Solution by PrepWiser.