Question

In the arrangement shown in the figure, the system is in equilibrium. Mass of the block $A$ is $M$ and that of the insect clinging to block $B$ is $m$. Pulley and string are light. The insect loses contact with the block $B$ and begins to fall. After how much time the insect and the block $B$ will have a separation $L$ between them.

• A. $\sqrt{\frac{M}{(2 M-m) L g}}$
• B. $\sqrt{\frac{(2 M-m) L}{M g}}$
• C. $\sqrt{\frac{(2 M+m) L}{M g}}$
• D. $\sqrt{\frac{M}{(2 M+m) L g}}$

Answer 1

Answer: (B)

Mass of block $A: m_A=M$
Mass of block $B ; m_B=M-m$
Acceleration of $B$ after the insect falls,
$a_B=\left(\frac{m_A-m_B}{m_A+m_B}\right) g(\uparrow)=\frac{m g}{2 M-m}$
Acceleration of the insect $=g(\downarrow)$
The two objects separate with a relative acceleration of
$ a=g+\frac{m g}{2 M-m}=\frac{2 M g}{2 M-m} $
$ \therefore \frac{1}{2} a t^2=L$
$\left(\frac{M g}{2 M-m}\right) t^2=L $
$ \Rightarrow t=\sqrt{\frac{(2 M-m) L}{M g}}$