devarshi-dt-logo

Question:

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

2Mω/(M+2m)

(M+2m)ω/2m

(M+2m)ω/M

Mω/(M+2m)

Solution:

As no external torque is acting about the axis, angular momentum of system remains conserved.
I₁ω₁ = I₂ω₂ ⇒ ω₂ = I₁ω₁/I₂
= Mr²ω/(M+2m)r² = Mω/(M+2m)