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Question

A car is moving with a speed of 72kmh−1. The radius of its wheel its 50cm. If its wheels come to rest after 20 rotations as a result of application of brakes, then the angular retardation produced in the car will be

A
23.5rads2
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B
0.25rads2
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C
6.35rads2
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D
zero
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Solution

The correct option is B 6.35rads2
Given,
v=72kmph=72518ms1
=20ms1.
Now , angular velocity of wheel intially=vr
where , r is radius of wheel.
r=50cm {given}
=0.5m
angular velocity intially=40rads1
and also given, That the wheel is rotated by 20revolutions.
angle of rotation say ( θ ) =20×2πrads1
θ=40πrads1
As we know that,
ω2finalω2intial=2×α×θ {let α be angular accerlation}
By substituting the known values,
02402=2×α×40π
α=6.3661rads1{- sign indicates retardation}
Therefore answer is Option C.

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