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"kgm"^(2)s^(-2)`
C. `2.86 "kgm"^(2)s^(-2)`
D. `6.66"kgm"^(2)s^(-2)`

Answer

D

Explanation

`v=54xx(5)/(18)=15 m//s, r=0.45m, I = 3"kgm"^(2)`
`t=15` sec
`omega=(v)/(r)=(15)/(0.45)=(100)/(3)` rad/sec
`alpha=(omega)/(t)=(100)/(3xx15)=(100)/(45)"rad/sec"^(2)`
`tau=Ialpha=3xx(100)/(45)=6.66"kg m"^(2)s^(-2)`