Question

Two identical blocks $A$ and $B$ of mass $m$ joined together with a massless spring as shown in the figure are placed on a smooth surface. If the block A moves with an acceleration $a_0$, then the acceleration of the block $B$ is

• A. $a_0$
• B. $-a_0$
• C. $\frac{f}{m}-a_0$
• D. $\frac{f}{m}$

Answer 1

The correct option is C $\frac{f}{m}-a_0$

Mass of the System $($ spring + blocks $)=2m$ since the spring is massless.

Acceleration of the CM$=a_{cm}=\frac{f}{2m}$

$a_{cm}=\frac{m_1{a}_1+m_2{a}_2}{m_1+m_2}$ ........(1)

$a_1=a_0$
Substituting $a_{cm}$ and $a_1$ in (1) we get,

$\frac{f}{2m}=\frac{m{a}_0+m{a}_2}{2m}$

$\Rightarrow a_2=\frac{f}{m}-a_0$;