A car is moving on a horizontal circular road | vedclass

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Question

(D) The maximum speed $v_{	ext{max}}$ for a car on a horizontal circular road is given by the condition that the centripetal force is provided by the

Vedclass · Accepted Answer

All of these

Vedclass · Answer

(D) The maximum speed $v_{	ext{max}}$ for a car on a horizontal circular road is given by the condition that the centripetal force is provided by the static friction: $\frac{mv^2}{r} \leq \mu mg$.Thus,$v^2 \leq \mu rg$.Given: radius $r = 0.1 \, km = 100 \, m$,coefficient of friction $\mu = 0.4$,and $g = 10 \, m/s^2$.Calculating the maximum speed: $v_{	ext{max}} = \sqrt{\mu rg} = \sqrt{0.4 	imes 100 	imes 10} = \sqrt{400} = 20 \, m/s$.Since the car can move at any speed less than or equal to the maximum speed without skidding,the speed can be any value $v \leq 20 \, m/s$.Therefore,$5 \, m/s$,$10 \, m/s$,and $20 \, m/s$ are all possible speeds.Hence,the correct option is $D$.

$A$ car is moving on a horizontal circular road of radius $0.1 \, km$ with constant speed. If the coefficient of friction between the tyres of the car and the road is $0.4$,then the speed of the car may be ......... $m/s$ $(g = 10 \, m/s^2)$.

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