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 (in kgm2s-2) transmitted by its brakes to the wheel is :
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answer is 6.67.
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Detailed Solution
Given : Speed V=54kmh-1=15 ms-1 Moment of inertia, I=3kgm2 Time, t =15 s ωi=Vr=150.45=1003 and ωf=0ωf=ωi+αt ⇒0=1003+(-α)(15) ⇒ α=10045 Average torque transmitted by brakes to the wheel τ=(I)(α)=3×10045=6.67kgm2 s-2