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Question

The system shown in the figure is released from rest. The spring gets elongated if:



Your Answer
A
M>m
Your Answer
B
M>2m
Your Answer
C
M>m2
Correct Answer
D
any value of M

Solution

The correct option is D any value of M
Net pulling force on the system of (3 blocks+spring+string) is (Mg+mg)mg=Mg
Total mass pulled =M+2m
Thus, acceleration of system:
a=MgM+2m downwards
MM+2m<1 always for all values of m and M
a<g, where a= acceleration of system.

a<g means that some opposing force is acting on block M in upward direction, which is spring force. If this force had not acted, then acceleration of mass M would be g downwards.
Elongation in spring will develop for any value of mass M.

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