A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30 "rad s"^(-1). What is angular velocity, if a mass of 0.25 kg is put on periphery of the disc ?

A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity

1.	A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30 "rad s"^(-1). What is angular velocity, if a mass of 0.25 kg is put on periphery of the disc ?
Answer» 24 RAD `s^(-1)` 36 rad `s^(-1)` 15 rad `s^(-1)` 26 rad `s^(-1)` Solution :If no external torque acts on a SYSTEM of PARTICLES, then angular momentum of the system remains constant, i.e., `tau=0` `rArr (dL)/(dt) = 0 rArr L = I omega =` constant `r rArrI_(1)omega_(1)=I_(2)omega_(2)rArr(1)/(2)Mr^(2)omega_(1)=(1)/(2)(M+2m)r^(2)omega_(2)`....(i) Here, `M=2kg,m=0.25kg,r=0.2m,omega_(1)=30 "rad s"^(-1)` Hence, we get after putting the given values in Eq. (i) `(1)/(2)xx2xx(0.2)^(2)xx30=(1)/(2)xx(2+2xx0.25)(0.2)^(2)xxomega_(2)` or `1.2=0.05omega_(2)or omega_(2)=24 "rad s"^(-1)`.