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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 :

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 mBy the law of conservation of linear momentum,m1v1+m2v2=m1v+m2v∴2×6+4×3=2v+4v∴12+12=6v∴v=4m/sBy 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∴108−96=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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