Question

The system shown is in equilibrium. Find the acceleration of the block A at the instant just after the spring between the ceiling and A is cut. All blocks are of equal masses ‘$m$’ each and the springs are of equal stiffness. (Assume springs to be ideal).

• A. Zero
• B. $2g$
• C. $g$
• D. $\frac{3g}{2}$

Answer 1

The correct option is D $\frac{3g}{2}$

Before culting
Since A and B are connected by inextensible string, therefore both will experience same acceleration. Hence they will be considered as single system.
Let the extension in the string between ceiling and block A be $x_1$ and that for spring between B and C be $x_2$
Before cutting,

For block C,
$\begin{array}{}K{x}_2=mg& \text{(1)}\end{array}$
For block A and B,
$K{x}_1=K{x}_2+2mg$
Since $K{x}_2=mg$
$\begin{array}{}\Rightarrow K{x}_1=3mg& \text{(2)}\end{array}$
After cutting, $K{x}_1=0$ and spring force on C will not change immediately.

Let $a$ be the acceleration of block A and B.
From the FBD of block A and B,
$K{x}_2+2mg=2ma$
$mg+2mg=2ma$ $\left[\text{Using}\right(1\left)\right]$
$\Rightarrow a_A=a_B=\frac{3g}{2}\downarrow$