A car of mass $1000 k g$ moves on a circular track of radius $20 m$ . If the coefficient of friction is $0.64$ , then the maximum velocity with which the car can move is

22.4 m / s

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5.6 m / s

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11.2 m / s

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Solution

The correct option is C $5.6 m / s$
Frictional force acting on the car $= μ \times m g$
$μ$ is friction coefficient
$F_{r} = 0.64 \times 1000 g = 640 g$
Centrifugal force on the car $= \frac{m v^{2}}{r}$
For the car to not slip, the centrifugal force should be less than the
$640 g \geq \frac{m v^{2}}{r}$
$640 g \geq \frac{1000 v^{2}}{20}$
$v^{2} \leq 12.8 g$
$v \leq 11.2 m / s$

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