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Question

The system shown is in equilibrium. Find the acceleration of the block C at the instant just after the spring between ceiling and A is cut. All blocks are of equal masses ‘m’ each and springs are of equal stiffness. (Assume springs to be ideal).

A
Zero
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B
2g
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C
g
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D
3g2
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Solution

The correct option is A Zero
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(1)
For block A and B,
Kx1=Kx2+2mg
Since Kx2=mg
Kx1=3mg(2)
When the spring between ceiling and A is cut , the spring force on C will not change immediately.
After cutting, FBD of C,

From the FBD of block C,
mgKx2=mac
mgmg=mac [Using (1)]
ac=0

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