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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 15s, the magnitude of average torque transmitted by its brakes to the wheel is :
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- 8.58 kg m² s-2
- 10.86 kg m² s-2
- 2.86 kg m² s-2
- 6.66 kg m² s-2
Correct Option: D
Given : Speed V = 54 kmh–1 = 15 ms–1
Moment of inertia, I = 3 kgm²
Time t = 15s
| ωi = | = | = | ωf = O | |||
| r | 0.45 | 3 |
ωf = ωi + αt
| 0 = | + (-α)(15) | |
| 3 |
| ⇒ | ||
| 45 |
Average torque transmitted by brakes to the wheel
| τ = (I) (α) = 3 × | = 6.66 kgm²s-2 | |
| 45 |
