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Question

Two solid cylinders connected with a short light rod about common axis have radius R and total mass M rest on a horizontal table top connected to a spring of spring constant k as shown. The cylinders are pulled to the left by x and released. There is sufficient friction for the cylinders to roll. Find time period of oscillation

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A
2πMk
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B
2πM2k
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C
2π3M2k
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D
2πM3k
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Solution

The correct option is B 2π3M2k

Here, τ=Iα=kx.R

or (MR22+MR2)α=kxR
or Rα=2k3Mx
now, a=Rα=2k3Mx
thus, ω=2k3M
Time period T=2πω=2π3M2k


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