Two masses A and B , each of mass M are fixed together by a...

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 :

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

Options

A
$\dfrac{MF}{F + Ma}$
B $\dfrac{F + Ma}{M}$
C $\dfrac{Ma - F}{M}$
D $\dfrac{F - Ma}{M}$

Correct answer

D. $\dfrac{F - Ma}{M}$

Step-by-step solution

${a}_{cm} = \dfrac{{m}_{1}{a}_{1} + {m}_{2}{a}_{2}}{{m}_{1} + {m}_{2}}$

$\dfrac{F}{2M} = \dfrac{Ma + M{a}_{B}}{2M}$

${a}_{B} = \dfrac{F - Ma}{M}$

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