A disc of radius `R` and mass `M` is plvoted at the rim and is set for small oscillation. if simple pendlum has to have the same period as that the of the disc, the length of the simple pendlum should to

Options

A. `(5)/(4)R`
B. `(2)/(3)R`
C. `(3)/(4)R`
D. `(3)/(2)R`

Answer

D

Explanation

Time period of a physical pendulum

`T = 2pi sqrt((I_(0))/(mgd)) = 2pi sqrt(((I_(0)/(mgd)mR^(2) + mR^(2)))/(mgR))`
`= 2pi sqrt((3R)/(2g))` ….(i)
`T_("simple pendulum") = 2pi sqrt((1)/(g))` ….(ii)
Equating (i) and (ii) `l = (3)/(2) R`.