In the figure, block 'A' of mass 'm' is attached to one end of a light spring and the other end of the spring is connected to another block 'B' of mass 2m through a light

Question

In the figure, block 'A' of mass 'm' is attached to one end of a light spring and the other end of the spring is connected to another block 'B' of mass 2m through a light string. 'A' is held and B is at rest in equilibrium. Now A is released. The acceleration of A just after that instant is 'a'. The same thing is repeated for 'B'. In that case the acceleration of ' B ' is ' b ', then value of $a / b$ is:

TestHub · Accepted Answer

When A is held, B is in equilibrium: spring force $k x = T = 2 m g$ .

Just after A is released the spring force on A is still $2 m g$ (upward): $2 m g - m g = ma \Rightarrow a = g$ .

Now hold B and let A hang in equilibrium: $T = k x = m g$ . Just after B is released the spring force is still $m g$ : $2 m g - m g = 2 mb \Rightarrow b = \frac{g}{2}$ .

$\frac{a}{b} = \frac{g}{g /2} = 2$ .

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