Question

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 $‘a^{\prime }$, then the acceleration of mass $B$ will be :

• A. $\frac{F+Ma}{M}$
• B. $\frac{F-Ma}{M}$
• C. $\frac{Ma-F}{M}$
• D. $\frac{MF}{F+Ma}$

Answer 1

The correct option is B $\frac{F-Ma}{M}$


On considering the two mass system, the acceleration of centre of mass, $a_{\text{com}}=\frac{F}{2M}$

Also,

$a_{\text{com}}=\frac{M_A{a}_A+M_B{a}_B}{M_A+M_B}$

$\Rightarrow \frac{F}{2M}=\frac{Ma+M{a}_B}{M+M}$

$\Rightarrow a_B=\frac{F-Ma}{M}$