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Question

A car moves on a horizontal track of radius r, the speed is increasing at a constant rate a, coefficient of friction between road and tyre is μ, the speed at which car will skid is

A
[(μ2g2+a2)r2]1/4
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B
μgr
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C
[(μ2g2a2)r2]1/4
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D
ar
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Solution

The correct option is C [(μ2g2a2)r2]1/4
Given, at=a
aC=V2r
(Here V keeps increasing due to at )
Fnet=(ma)2+(mV2r)2
For the car to just start skidding,
Fnet=μ mg

μ mg=(ma)2+(mV2r)2
μ2g2=a2+(V4r2)

Solving for V,
V=[(μ2g2a2)r2]14

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