A conducting rign of mass 100 gram and radius `0*5m` is placed on a smooth horizontal plane. The ring carries a current of `I=4A`. A horizontal magnetic field `B=10T` is switched on at time `t=0` as shown in figure. The initial angular acceleration of the ring is

Options

A. `200pi rad//s^2`
B. `400pi rad//s^2`
C. `800pi rad//s^2`
D. `1200pi rad//s^2`

Explanation

Here, mass of ring, `m=100g=0*1kg`,
radius of ring, `R=0*5m`, `I=4A`, `B=10T`
Magnetic moment of ring, `M=I(piR^2)`
acting perpendicular to the plane of ring.
Torque on the ring due to current
`tau=MBsin 90^@=IpiR^2B`
Moment of inertia of ring, about an axis of rotation tangent to the ring
`I^'=1/2mR^2`
If `alpha` is the initial angular acceleration of the ring, then initial torque on ring
`tau^'=I^'alpha=1/2mR^2xxalpha`
`:. 1/2mR^2alpha=IpiR^2B`
or `alpha=(2IpiB)/(m)=(2xx4xxpixx10)/(0*1)=800pi rad//s^2`