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Question

An ideal massless spring S can be compressed by 1 m by a force of 100 N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane at 30 to the horizontal. A 10 kg block M is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by 2 m. If g=10 m/s2, what is the speed of mass just before it touches the spring?

A
20 m/s
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B
30 m/s
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C
10 m/s
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D
40 m/s
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Solution

The correct option is A 20 m/s
F=kx
k=Fx=1001 N/m=100 N/m
Now from energy conservation, between natural length of spring and its maximum compression state.
12mv2+mgh=12kx2max
where h is the height of the block when it just touches the spring from the point where the maximum compression occurs.
v=kx2maxm2gh
=(100)(2)210(2)(10)(22)
=20 m/s

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