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Question

A circular disc of mass M and radius R is connected to spring and placed on rough surface. The friction is sufficient for pure rolling. When the disc is slightly displaced and released, it executes simple harmonic motion.

Let μ be the coefficient of friction between the disc and ground, the amplitude A of oscillations for which no slipping occurs is

A
0<A<4μMgK
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B
A>3μMgK
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C
amplitude A must be less than μMgK
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D
0<A<3μMgK
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Solution

The correct option is D 0<A<3μMgK
Ff=mafR=mR2α2f=ma2F=3ma2F=3ff=F3f=Kx3X=acosωtf=KA3cosωtμmg=KA3A=3μmgK
0<A<3μmgK; for no slipping
a=2F3m=2Kx3mT=2π3m2kWf=0

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