# 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 m2. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is : Option 1) 8.58 kg m2 s-2 Option 2) 10.86 kg m2 s-2 Option 3) 2.86 kg m2 s-2 Option 4) 6.66 kg m2 s-2

As we learned in concept

Analogue of second law of motion for pure rotation -

- wherein

Torque equation can be applied only about two point

(i) centre of motion.

(ii) point which has zero velocity/acceleration.

V=54 Km/hr = 15m/s

Angular velocity of vehicle V=W0r

Angular Accn

=>

Option 1)

8.58 kg m2 s-2

This option is incorrect.

Option 2)

10.86 kg m2 s-2

This option is incorrect.

Option 3)

2.86 kg m2 s-2

This option is incorrect.

Option 4)

6.66 kg m2 s-2

This option is correct.

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