A block 'A' of mass 'm' is attached at one end of a light spring and the other end of the spring is connected to another block 'B' of mass 2 m through a light string as shown in the figure.'A' is held and B is in static equilibrium. Now A is released. The acceleration of A just after that instant is 'a'. In the next case, B is held and A is in static equilibrium. Now when,B is released, its acceleration immediately after the release is 'b'. The value of a/b is: (Pulley, string and the spring are massless)

Moderate

Solution

For first case tension in spring will be
$T_{s} = 2 mg just after' A' is released .$
2mg-mg = ma $\Rightarrow a = g$
In second case $T_{s} = mg$
$2 mg - mg = 2 mb$
$b = \frac{g}{2}$
$\frac{a}{b} = 2$

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