A cyclist on a level road takes a sharp circular turn of radius $$3m$$ (g=10ms-2). If the coefficient of static friction between the cycle tyres and the road is $$0.2$$, at which of the following speeds will the cyclist not skid while taking the turn ?

Question

A cyclist on a level road takes a sharp circular turn  of radius $$3m$$ (g=10ms-2). If the coefficient of static friction between the cycle tyres and the road is $$0.2$$,  at which of the following speeds will the cyclist not skid while taking the turn ?

Infinity Learn · Accepted Answer

Vmax  $$=$$  μgr  $$=$$  $$0.2$$  ×  $$10$$  ×  $$3$$  $$=$$   $$6$$  $$m/s$$  $$=$$  $$2.45$$  $$m/sVmax$$  $$=$$ $$8.8$$   $$km/hr$$∴  With $$7.2$$ km $$h-1$$ the cyclist will not skid.

Circular motion in horizontal plane

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A cyclist on a level road takes a sharp circular turn of radius 3m ( $g = 10 m s^{- 2}$ ). If the coefficient of static friction between the cycle tyres and the road is 0.2, at which of the following speeds will the cyclist not skid while taking the turn ?

$\begin{array}{l} V_{\max} = \sqrt{μ g r} = \sqrt{0.2 \times 10 \times 3} = \sqrt{6} m / s = 2.45 m / s \\ V_{\max} = 8.8 k m / h r \end{array}$
$∴$ With $7.2 k m h^{- 1}$ the cyclist will not skid.

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