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A disc of radius R and mass M is pivoted...

A disc of radius `R` and mass `M` is pivoted at the rim and it set for small oscillations. If simple pendulum has to have the same period as that of the disc, the length of the simple pendulum should be

A

`(5//4)R`

B

`(2//3)R`

C

`(3//4)R`

D

`(3//2)R`

Text Solution

Verified by Experts

Time period of a physical pendulum :
`T=2pisqrt((I_(0))/(mgd))=2pisqrt((((1)/(2)mR^(2)+mR^(2)))/(mgR))=2pisqrt((3R)/(2g))`.....`(1)`
`T_("simple pendulum")=2pisqrt((l)/(g))`……….`(2)`
Equating Eqs.`(1)` and `(1)`, `l=(3)/(2)R`.
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