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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 is set for small oscillations about an axis pendicluar to plane of disc. If a simple pendulum has to have the same time period as that of the disc, the length of the pendulum should be

A

(5/4) R

B

(2/3) R

C

(3/4) R

D

(3/2) R

Text Solution

Verified by Experts

The correct Answer is:
D
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.
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