Question

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

• A. $\frac{\left(F+\hspace{0.17em}Ma\right)}{M}$
• B. $\frac{\left(F-Ma\right)}{M}$
• C. $\frac{\left(Ma-F\right)}{M}$
• D. $\frac{MF}{\left(F+Ma\right)}$

Answer 1

The correct option is B

$\frac{\left(F-Ma\right)}{M}$

Step 1: Given data

Mass of A and B are both $M$

Force is $F$

Acceleration of mass A is $a$

Step 2: Calculation

Here for block A,

We know, the force due to spring,

$F=kx$

Here,

$$\begin{gathered} F=kx \\ \Rightarrow ma=kx \\ \Rightarrow a=\frac{kx}{M}-------\left(1\right) \end{gathered}$$

Here for block B,

$a_B=\frac{(F-kx)}{M}-----\left(2\right)$

Where $F$ is the force acting on B

From equations (1) and (2)

$a_B=\frac{F}{M}-\frac{kx}{M}$

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

$a_B=\frac{\left(F-Ma\right)}{M}$

The acceleration of mass B will be $\frac{\left(F-Ma\right)}{M}$.

Hence, option B is correct.