Question

The system shown is in equilibrium. Find the accelerations of the blocks A, B and C just after the spring between B and C is cut. All blocks are of equal masses $‘m^{\prime }$ each and springs are of equal stiffness. (Assume springs to be ideal and take downward acceleration to be positive).

• A. $+g,+g,-g$
• B. $-\frac{g}{2},-\frac{g}{2},+g$
• C. $+g,-\frac{g}{2},-g$
• D. $0,-\frac{g}{2},-g$

Answer 1

The correct option is B $-\frac{g}{2},-\frac{g}{2},+g$

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,
$K{x}_2=mg$
For block A and B,
$K{x}_1=k{x}_2+2mg$
Since $K{x}_2=mg$
$\Rightarrow K{x}_1=3mg$

After Cutting, spring force $k{x}_2=0$

Let $a$ be the acceleration of block A and B.
For block A and B,
$K{x}_1-2mg=2ma$
Since $K{x}_1=3mg$
$\Rightarrow 3mg-2mg=2ma$
$a=\frac{g}{2}$ (Upwards) $\Rightarrow a_B=a_C=-\frac{g}{2}$
Let the acceleration for block C be $a_c$, then from the free body diagram,
$mg=m{a}_c$
$a_c=g$ (Downwards)