A uniform semicircular disc of mass ' M ' and radius ' R ' hinged at point O shown in figure is released from rest from a vertical position as shown. If the initial magnitude of angular acceleration of the disc is (x g/3 π R), then the value of x is (Center of mass is at a distance (4 R/3 π) from center of disc)

Question

A uniform semicircular disc of mass ' M ' and radius ' R ' hinged at point O shown in figure is released from rest from a vertical position as shown. If the initial magnitude of angular acceleration of the disc is (x g/3 π R), then the value of x is (Center of mass is at a distance (4 R/3 π) from center of disc) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

τ=I α ; τ=m g((4 R/3 π)) ; I=(M R2/2), α=(8 g/3 π R) ⇒ x=8

τ=Iα;τ=mg(3π4R​);I=2MR2​, α=3πR8g​ ⇒x=8

$τ = I α; τ = m g (\frac{4 R}{3 π}); I = \frac{M R ^{2}}{2},$
$α = \frac{8 g}{3 π R}$
$\Rightarrow x = 8$