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Question

# Two blocks A and B of masses m & 2m placed on smooth horizontal surface are connect with a light spring. The two blocks are given velocities as shown when spring is at natural length. Find maximum extension in the spring.

A
2mkv
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B
4mkv
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C
6mkv
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D
mkv
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Solution

## The correct option is C √6mkvGiven that, m1=m m2=2m Reduced mass of the system. μ=m1m2m1+m2 ⇒μ=m×2mm+2m ⇒μ=2m3 External force on the system is zero. So energy of the system is conserved. Let maximum extension in the string is x. 12μv2r=12kx2 ⇒12×2m3(3v)2=12kx2 ⇒x=√6mkv

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