JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Laws of Motion

A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be

30 m / s

without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be _____

m / s

Answer: 24

Solution

On a flat road the centripetal force needed to round a bend is supplied entirely by friction, so at the skidding limit

\frac{m v _{m a x}^{2}}{R} = μ m g

, giving

v_{m a x} = μ R g

. With

μ

and

g

unchanged the maximum speed scales as

R

, so

\frac{v _{2}}{v _{1}} = \frac{R _{2}}{R _{1}} = \frac{48}{75} = \frac{16}{25} = \frac{4}{5}

, and therefore

v_{2} = 30 \times \frac{4}{5} = 24 m s^{- 1}

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Integer answer

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