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 figure. If the mass A starts moving away from mass B with acceleration ‘a’, then the acceleration of mass B will be:

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$\frac{M a - F}{M}$

$\frac{M F}{F + M a}$

$\frac{F + M a}{M}$

$\frac{F - M a}{M}$

answer is D.

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Detailed Solution

$\begin{array}{l} For mass + spring system, F = (M + M) a_{c m} \\ \Rightarrow a_{c m} = \frac{F}{2 M} (towards l e f t) \\ Now, using a_{c m} = \frac{m_{1} a_{1} + m_{2} a_{2}}{m_{1} + m_{2}} \\ \Rightarrow \frac{F}{2 M} = \frac{M (a) + M a_{B}}{2 M} \\ \Rightarrow a_{B} = \frac{F - M a}{M} \end{array}$

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