An automobile moves on a road with a speed of 54 km $h^{-1}$.  The radius of its wheels 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 transmitted by its brakes to the wheel is

detailed solution

Correct option is C

Here,speed of the automobiles,v=54 km h-1=54×518 m s-1=15 m s-1.Radius of the wheel of the automobile, R=0.45 m Moment of inertia of the wheel about its axis of rotation, I=3 kg m2Time in which the vehicle brought to rest, t = 15 s.  The initial angular speed of the wheel isωi=vR=15 m s-10.45 m=150045rads-1=1003rads-1and its final angular speed is ωf=0   (as the vehicle comes to rest) ∴ The angular retardation of the wheel is α=ωf-ωit=0-100315 s=-10045rads-2 The magnitude of required torque is τ=I|α|=3 kg m210045rads-2=203 kg m2 s-2=6.66 kg m2 s-2