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Question

An automobile moves on a road with a speed of $$54 \,km h^{-1}$$. The radius of its wheel is $$0.45\, m$$ and the moment of inertia of the wheel about its axis of rotation is $$3 \,kg m^2$$. If the vehicle is brought to rest in $$15\, s$$, the magnitude of average torque transmitted by its brakes to the wheels is:


A
2.86kgm2s2
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B
6.66kgm2s2
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C
8.58kgm2s2
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D
10.86kgm2s2
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Solution

The correct option is B $$6.66\, kg\, m^2\, s^{-2}$$
Torque $$=$$ moment of inertia $$\times $$ angular momentum
or $$\tau=I\alpha$$
or $$\displaystyle \tau=I\frac{a}{r}=I\frac{v}{tr}=3\frac{(\frac{54\times 1000}{3600})}{15\times 0.45}=6.66  kg m^2 s^{-2}$$

Physics

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