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

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((l_(0))/(mg d)) = 2pi sqrt(((1)/(2) mR^(2) + mR^(2))/(mgR)) = 2pi sqrt((3R)/(2g))` ….(a)
`T_("simple pendulum") = 2pi sqrt((l)/(g))`
Equating (a) & (b), `l = (3)/(2) R`
Hence (D) is correct.