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Question

Two blocks of masses 3 kgand 6 kg respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant k=200N/m. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. Find the maximum extension of the spring.

A
30 cm
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B
60 cm
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C
15 cm
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D
90 cm
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Solution

The correct option is A 30 cm
Here reduced mass μ=6×36+3=2 kg

Initial kinetic energy of system w.r.t CM
(Ki)cm=12mM(m+M)V2rel=(2(1))2=9 J

At maximum extension Vrel=0

Final kinetic energy of system w.r.t CM
(Kf)cm=0

Now, using WE theorem in COM frame
Ki+Ui=Kf+Ut
9+0=0+12Kx2
9=100x2
x=0.3 m=30 cm

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