A disc of radius R and mass M is pivoted at the rim and is 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

Question

A disc of radius R and mass M is pivoted at the rim and is 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

Tardigrade Admin · Accepted Answer

Time period of a physical pendulum <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/f7b1593ccd7fb7c16cf0e6b9d0e8295c-.png" /> T=2 π √(I0/m g d)=2 π √(((1/2) m R2+m R2)/m g R) =2 π √(3 R/2 g) .....(i) T text simple pendulum =2 π √(l/g) ...(ii) Equating (i) and (ii), l=(3/2) R.

Q. A disc of radius $R$ and mass $M$ is pivoted at the rim and is 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

$\frac{5}{4} R$

$\frac{2}{3} R$

$\frac{3}{4} R$

$\frac{3}{2} R$

Time period of a physical pendulum

T $= 2 π \frac{I _{0}}{m g d} = 2 π \frac{( \frac{1}{2} m R ^{2} + m R ^{2} )}{m g R}$
$= 2 π \frac{3 R}{2 g}$ .....(i)
$T_{simple pendulum} = 2 π \frac{l}{g}$ ...(ii)
Equating (i) and (ii), $l = \frac{3}{2} R$ .

Q. A disc of radius R and mass M is pivoted at the rim and is 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

45​R

32​R

43​R

23​R