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Question

A solid disk of radius R is suspended from a spring of linear spring constant k and torsional constant C, as shown in figure. In terms of k and C, what value of R will give the same period for the vertical and torsional oscillations of this system?


A
2Ck
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B
C2k
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C
2Ck
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D
12Ck
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Solution

The correct option is A 2Ck

Time - period (T) for linear SHM
T=2πmk ...(i)


Time - period (T) for angular SHM
T=2πIC ...(ii)
For disc

IC=mR22
From (i) and (ii)
2πmk=2πmR22C
mk=mR22C
R=2Ck
Hence, option (A) is correct.

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