Question

A four -wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in 10 s, the braking torque (in Nm) on each wheel is

• A. 10

Answer 1

The correct option is A 10
Initial velocity,

$u=\omega r=10\times 0.2=2m/s$

For vehicle to stop,

$v=u-at$

$\Rightarrow 0=u-at$

$\therefore a=\frac{u}{t}=\frac{2}{10}=0.2m/s^2$

Braking force = Total mass $\times$ deceleration

$F=1000\times 0.2=200N$

$F_{\text{each wheel}}=\frac{200}{4}=50N$

Braking torque on each wheel

$=50\times 0.2=10Nm$