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Question

Two blocks of masses m1=2kg and m2=4kg are moving in the same direction with speeds v1=6m/s and v2=3m/s, respectively on a frictionless surface as shown in the figure. An ideal spring with spring constant k=30000N/m is attached to the back side of m2. Then the maximum compression of the spring after collision will be :
156829_4ab6b73c430a4f45a3f8b0a5c2d54be5.png

A
0.06 m
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B
0.04 m
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C
0.02 m
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D
None of these
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Solution

The correct option is C 0.02 m
By the law of conservation of linear momentum,

m1v1+m2v2=m1v+m2v

2×6+4×3=2v+4v

12+12=6v

v=4m/s

By the law of conversation of energy,
12m1v21+12m2v22=12(m1+m2)v2+12kx2

2×(6)2+4×(3)2=(2+4)(4)2+kx2

72+36=96+kx2

10896=kx2

12=30,000x2

x=1230,000

x=12,500

x=150

x=0.02m

x=2cm

option (A) is correct.

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