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

Answer

B

Explanation

`V=54(km)/(h)=15m//s`
`omega_(0)=(v)/(r)=(15)/(.45)(rad)/(s),omega=0`
`omega=omega_(0)+alphat`
`0=(15)/(.45)+alpha15`
`alpha=-(15)/(.45xx15)=-(1)/(.45)(rad)/(s^(2))`
`tau=I alpha=(3)/(.45)=-(300)/(45)=-6.66kgm^(2)//s^(2)`