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A mass of 0.5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be:

a
0.15 m
b
0.12 m
c
1.5 m
d
0.5 m

detailed solution

Correct option is A

By the law of conservation of energy, i.e.,     ΔK+ΔU=0    0−12mv2+12kx2−0=012mv2=12kx2⇒ x2=mv2k⇒ x=mv2k⇒ x=0.5×1.5×1.550∴=0.15m

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Two similar springs P and Q have spring constants Kp and KQ such that Kp > KQ. They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs WP and WQ are related as, in case (a) and case (b), respectively.


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