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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 each and springs are of equal stiffness. (Assume springs to be ideal and take downward acceleration to be positive).

A
+g,+g,g
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B
g2,g2,+g
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C
+g,g2,g
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D
0,g2,g
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Solution

The correct option is B g2,g2,+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 x1 and that for spring between B and C be x2
Before cutting

For block C,
Kx2=mg
For block A and B,
Kx1=kx2+2mg
Since Kx2=mg
Kx1=3mg

After Cutting, spring force kx2=0

Let a be the acceleration of block A and B.
For block A and B,
Kx12mg=2ma
Since Kx1=3mg
3mg2mg=2ma
a=g2 (Upwards) aB=aC=g2
Let the acceleration for block C be ac, then from the free body diagram,
mg=mac
ac=g (Downwards)

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