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Question

A motor car has a width 1.1 m between wheels. Its centre of gravity is 0.62 m above the ground and the coefficient of friction between the wheels and the road is 0.8. What is the maximum possible speed, if the centre of gravity inscribes a circle of radius 15 m ? (Road surface is horizontal)

A
11.23 m/s
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B
10.84 m/s
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C
7.64 m/s
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D
6.28 m/s
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Solution

The correct option is B 10.84 m/s
Given:
Width of the car, d=1.1 m,
Radius of the circular road,R=15 m
Friction acting on the surface of the road,μ=0.8
Let us consider the velocity of the car be v
Maximum centripetal force provided by friction will be =μmg
The frictional force is balanced by the centrifugal force acting outward.
Therefore,
μmg=mv2R

v=μ g R
Substituting all the values we get,

v=0.8×9.8×15

v=10.84 m/s

Hence, option (C) is correct.

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