A cyclist rides along the circumference of a circle in a horizontal plane of radius R , the friction coefficient being dependent only on distances r from the centre O of the plane as μ = μ 0 ( 1 − R r ) , where μ 0 is a constant. If the radius of the circle with the centre at the point O along which the cyclist can ride with the maximum velocity if 6 nR , find n.

Maximum speed on a circle of radius r : v 2 = μg r = μ 0 g r ( 1 − R r ) . Maximize: d r d [ r ( 1 − R r ) ] = 1 − R 2 r = 0 ⇒ r = 2 R . Given r = 6 n R : 6 n = 2 1 ⇒ n = 3

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Physics - Circular Motion Question with Solution | TestHub

PhysicsCircular MotionDynamicsMedium2 minQB

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A cyclist rides along the circumference of a circle in a horizontal plane of radius R , the friction coefficient being dependent only on distances r from the centre O of the plane as $μ = μ_{0} (1 - \frac{r}{R})$ , where $μ_{0}$ is a constant. If the radius of the circle with the centre at the point O along which the cyclist can ride with the maximum velocity if $\frac{nR}{6}$ , find n.

Answer:

Solution:

Maximum speed on a circle of radius $r$ : $v^{2} = μg r = μ_{0} g r (1 - \frac{r}{R})$ .

Maximize: $\frac{d}{d r} [r (1 - \frac{r}{R})] = 1 - \frac{2 r}{R} = 0$ ⇒ $r = \frac{R}{2}$ .

Given $r = \frac{n R}{6}$ : $\frac{n}{6} = \frac{1}{2}$ ⇒ $n = 3$

Stream:JEESubject:PhysicsTopic:Circular MotionSubtopic:Dynamics

⏱ 2mℹ️ Source: QB

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