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Question

A spring is loaded with two blocks m1 and m2 where m1 is rigidly fixed with the spring and m2 is just kept on the block m1 as shown in the figure. The maximum energy of oscillation that is possible for the system having the block m2 in contact with m1 is


A

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B

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C

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D

(m1+m2)2g2k

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Solution

The correct option is C


Let the required amplitude be A. For this amplitude of oscillation the normal contact force between the blocks can be given as

m2g−N=m2a where a=ω2A

⇒m2g−N=m2ω2A

Putting N = 0 for just losing contact for maximum amplitude, we obtain

A=gω2 where ω = angular frequency of oscillation of (m1+m2) and the spring.

Putting ω2=km1+m2, we obtain

A=(m1+m2)gk

∴Umax=12kA2=(m1+m2)2g22k


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