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Question

A car of mass 800 kg moves on a horizontal circular track of radius 40 m. If the coefficient of static friction (μs) is 0.5, then the maximum velocity with which the car can move will be

A
15 m/s
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B
20 m/s
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C
25 m/s
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D
14 m/s
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Solution

The correct option is D 14 m/s
For this case, the road is an unbanked horizontal circular track, hence friction is the only source of centripetal force (Fc).

Fc=mv2r..........(1)

Vertical forces on the body are balanced, since ay=0
i.e N=mg........(2)

For executing circular motion successfully:
Fcfmax..............(3)

From Eq.(1) and (3):
mv2rfmax
or mv2rμsmg
vμsgr

vmax=μsgr
=0.5×9.8×40=14 m/s

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