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Question

A light spring of force constant K is held between two blocks of masses m and 2m. The two blocks and the spring system rests on a smooth horizontal floor. Now the blocks are moved towards each other compressing the spring by x and then they are suddenly released. The relative velocity between the blocks when the spring attains its natural length will be

A
(3K2m)x
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B
(2K3m)x
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C
(K3m)x
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D
(K2m)x
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Solution

The correct option is A (3K2m)x
Potential energy of the spring is being converted into kinetic energy of system.

Potential energy of the spring before released =12Kx2

K.E of the system in Center of mass frame =12μv2relative

where, μ=m×2mm+2m=2m3 is reduced mass of the system.
Now, 12μv2relative=12Kx2

v2relative=32mKx2

vrelative=(3K2m)x

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