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Question

In the arrangement shown, the solid cylinder of mass m is slightly rolled to the left and released. It starts oscillating on the horizontal surface without slipping. Then time period of oscillation is
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A
π3Km
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B
2π3M2K
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C
2π2K3M
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D
2π3K2m
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Solution

The correct option is B 2π3M2K
Torque=f(R) R Radius of cylinder
I=fR moment of inertia for solid cylinder
As no slipping I=12mR2
a=R
12mR2(aR)=fRf=12ma
ma=kxf=kx12ma
kx=32mad2xdt2+23kmx=0
It is of form d2xdt2+w2x=0
w=23km
T=2πw=2π32mR


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