Question

System shown in the diagram is in equilibrium. Suddenly string between A and B is cut, then initial acceleration of B is :

• A. $g$ downward
• B. $3g$ downward
• C. $2g$ downward
• D. $zero$

Answer 1

The correct option is C $2g$ downward

Let the tension in the uppermost spring be $T$ and string $AB$ be $T_1$

Equation of motion for the uppermost block is,

$T=T_1+mg$

Similarly, equation of motion for the block between $AB$.

$T_1=T_2+mg$.

Also, equation of block at $C$-

$T_2=mg$.

When the string $AB$ is cut $T_1$ becomes zero,and the acceleration with which the second block falls is $\frac{T_2+mg}{m}=\frac{mg+mg}{m}=2g$.

This force on the block acts downwards and hence the acceleration of the block is in downward direction.

Hence, the option is $C$.