Two blocks of masses m1 = 2 kg and m2 = 5 kg are moving in the same direction along a frictionless surface with speeds 10 ms-1 and 3ms-1 respectively. An ideal spring with K=1120Nm-1 is attached to the back side of m2. Find the maximum compression of the spring when the blocks collide.
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a
0.50 m
b
0.25 m
c
0.75 m
d
1 m
answer is B.
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Detailed Solution
Using conservation of linear momentumm1×10+m2×3=m1+m2VCM2×10+5×3=7 VcMVCM=5 m s-1At maximum compression of spring both particles will acquire common velocity VCM=5 m s-1 Energy conservation127×52+12kx2⇒12kx2=12×2×102+12×5×32-12×7×52⇒x=0.25 m