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Question

The velocity of a car travelling on a straight road is 36kmh1 at an instant of time. Now travelling with uniform acceleration for 10 s, the velocity becomes exactly double. If the wheel radius of the car is 25 cm, then which of the following numbers is the closest to the number of revolutions that the wheel makes during this 10 s?

A
84
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B
95
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C
126
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D
135
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Solution

The correct option is C 95
Radius of wheel r=25 cm =0.25 m
Initial velocity of car u=36km/h=36×518=10m/s
Thus initial angular speed of wheel wi=ur=100.25=40 rad/s
Final velocity of car v=2u=20m/s
Final angular speed of wheel wf=vr=200.25=80 rad/s
Using wf=wi=αt where t=10 s
80=40+α(10) α=4 rad/s2
Using θ=wit+12αt2
We get θ=(40)(10)+12(4)(10)2=600 rad
Thus number of revolutions n=θ2π=6002π=95.54 revoltions
Thus about 95 revolution were made by the wheel.

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