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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/sFor 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: Fc≤fmax..............(3) From Eq.(1) and (3): mv2r≤fmax or mv2r≤μsmg ∴ v≤√μsgr ⇒vmax=√μsgr =√0.5×9.8×40=14 m/s

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