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Question

An automobile moves on a rough road with a speed of 54 kmh1. 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 wheel is brought to rest in 15 s, then find magnitude of average torque transmitted by the brakes to wheel. Assume no slipping at all points of contact.

A
10.86 kg m2 s2
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B
2.86 kg m2 s2
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C
6.67 kg m2 s2
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D
8.58 kg m2 s2
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Solution

The correct option is C 6.67 kg m2 s2
Assuming the wheels are in state of pure rolling on the road and v is the translational speed of COM of the wheel.

v=rω ...(i) ; condition of pure rolling
r=0.45 m, v=54 kmh1=15 ms1, I=3 kg.m2


Since
τ=Iα=Idωdt
τavg=I×ΔωΔt ...(ii)
From Eq (i) initially angular speed of wheel ωi=vr=150.45
Final angular speed of wheel after applying brakes ωf=0
From Eq (ii):
τavg=3×(0150.45)15
|τavg|=10015=6.66 kg m2 s2

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