Initial angular velocity of a circualr disc of mass M is `omega_1.` The tow sphere of mass ma re attached gently to diametrically opposite points ont eh edge of the disc. What is the final angular velocity on the disc?

Options

A. `((M+m)/(M))omega_1`
B. `((M+m)/(M))omega_1`
C. `((M)/(M+4m))omega_1`
D. `((M)/(M+2m))omega_1`

Answer

C

Explanation

(c ) When two small sphere of mass m are attached gently,
the external torque, about the axis of rotatation, is zero
and therefore the angular momentum about the axis fo
rotation is constant.
`:. I_1 omega_1 = I_2omega_2 rArr omega_2 = (1_1)/(I_2) omega_1`
Here I_1 = (1)/(2)MR^2 and I_2 = (1)/(2)MR^2 + 2mR^2`
`:. omega_2 = ((1)/(2)MR^2)/((1)/(2)MR^2 + 2mR^2 xx omega_1 = (M)/(M+4m) omega_1`