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Question

In the figure given below, block A is of mass m and block B is of mass 2m. The spring has force constant k. All the surfaces are smooth and the system is released from rest with the spring unstretched. Maximum extension in the spring is



Your Answer
A
mg2k
Correct Answer
B
4mgk
Your Answer
C
2mgk
Your Answer
D
mg4k

Solution

The correct option is A 4mgk
At maximum extension (xm) in the spring :
vA=vB=0
Applying conservation of mechanical energy :
Decrease in gravitaitonal potential energy of block B = Increase in elastic ptotential energy of spring.
 mBgxm=12Kx2m
(displacement of block B will be equal to the extension in spring)
or 2mgxm=12Kx2m
xm=4mgK

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