Question

An automobile moves on a road with a speed of $54km{h}^{-1}$. The radius of its wheel is $0.45m$ and the moment of inertia of the wheel about its axis of rotation is $3kg{m}^2$. If the vehicle is brought to rest in $15s$, the magnitude of average torque transmitted by its brakes to the wheels is:

• A. $2.86kg{m}^2{s}^{-2}$
• B. $6.66kg{m}^2{s}^{-2}$
• C. $8.58kg{m}^2{s}^{-2}$
• D. $10.86kg{m}^2{s}^{-2}$

Answer 1

The correct option is B $6.66kg{m}^2{s}^{-2}$

Torque $=$ moment of inertia $\times$ angular momentum

or $\tau =I\alpha$

or $\tau =I\frac{a}{r}=I\frac{v}{tr}=3\frac{\left(\frac{54\times 1000}{3600}\right)}{15\times 0.45}=6.66kg{m}^2{s}^{-2}$