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  4. 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) <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/13cf29f18282969210c37743b102faa3-.png />

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Q. 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)
image

Laws of Motion

Solution:

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