A circular disc `A` of radius `r` is made from an iron plate of thickness `t` and another circular disc `B` of radius `4r` is made from an iron plate of thickness `t//4`. Equal torques act on the discs `A` and `B`, initially both being at rest. At a later instant, the linear speeds of a point on the rim of `A` and another point on the rim of `B` are `v_(A)` and `v_(B)`, respectively. We have

Options

A. `v_(A) gt v_(B)`
B. `v_(A) = v_(B)`
C. `v_(A) lt v_(B)`
D. The relation depends on the actual magnitude of the torques.

Explanation

`m_(A)=rhoxxpir^(2)t=m`
`m_(B)=rhoxxpi(4r)^(2)(t)/(4)=4m`
`I_(A)=(1)/(2)mr^(2)=I,I_(B)=(1)/(2)xx4m(4r)^(2)=64I`
`alpha_(A)=(tau)/(I)=alpha_(0), alpha_(B)=(tau)/(64I), omega=0+alphat`
`v_(A)=omega_(A)r=alpha_(0)rt`
`v_(B)=omega_(B)4r=(alpha_(0)rt)/(16)`