An autmobile moves on road with a speed of `54 km//h`. The radius of its wheel is `0.45 m` and the moment of inertia of the wheel about its axis of rotation is `3 kg m^(2)`. If the vehicle is brought to rest in `15 s`, the magnitude of average torque tansmitted by its brakes to the wheel is :

Options

A. `8.58 kg m^(2) s^(-2)`
B. `10.86 kg m^(2) s^(-2)`
C. `2.86 kg m^(2) s^(-2)`
D. `6.66 kg m^(2) s^(-2)`

Answer

D

Explanation

`v= 54 xx (5)/(18) = 15m//s, r= 0.45m, I= 3 kg m^(2)`
t= 15 sec
`omega = (v)/(r) = (15)/(0.45) = (100)/(3)` rad/sec
`alpha = (omega)/(t) = (100)/(3 xx 15) = (100)/(45)` rad/`sec^(2)`
`tau= I alpha = 3 xx (100)/(45) = 6.66 kg m^(2) s^(-2)`