A solid cylinder of mass M and radius R is connected to spring of force constant k as shown in fig. Cylinder rolls without slipping on the horizontal surface. Its time period of oscillation is

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T=2π2M3K

T=2π2MK

T=2πM3K

T=2π3M2K

answer is D.

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Detailed Solution

Total energy 12Mu21+K2R2+12Kx2=constant12Mu21+12+12Kx2=constantMududt32+Kxdxdt=0Mududt32+Kxu=03M2a+Kx=0w=2k3M T=2πw=2π3M2K

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