Question

The system shown in equilibrium. Find the ratio of acceleration of the blocks $A$ and $B$ at the instant when the spring between ceiling and $A$ is cut. All the blocks have equal mass and the springs are ideal.

Answer 1

c) When the spring is cut b/w the blocks A and ceiling, blocks will have a pull equal to $k\times \Delta x$ where $\Delta x$ is extension in spring between A and B
From force equilibrium before the spring is cut
$k\Delta x=3mg\Rightarrow \Delta x=\frac{3mg}{k}$
The masses A and B will move with same acceleration as the string is taught between them
$a_{net}=\frac{totalforce}{totalmass}=\frac{mg+mg-k\times \frac{3mg}{k}}{2m}=\frac{g}{2}$ upwards
writing Equation of motion for block B
$T-mg=m{a}_{net}\Rightarrow T=mg+mg/2=3mg/2$
acceleration of C will be equal to gravity as the only force acting on it is of gravitational pull
$a_C=0g$ downwards