A circular racetrack of radius 300 m is banked at an angle of `15^(@)` If the coefficient of friction between the wheels of a race car and the road is 0.2 what is the (a) optimum speed of the race car to avoid wear and tear on its tyres , and (b) maximum permissible speed to aviod slipping ?

Options

A. `49.2ms^(-1)`
B. `38.1ms^(-1)`
C. `36.3ms^(-1)`
D. `48.3ms^(-1)`

Answer

B

Explanation

Given ,radius, r 300m
angle,`theta=15^@`
Coefficient of friction, `mu_(s)=0.2`
The maximum permissible speed `v_(max)`is given by equation.
`v_(max)= (rg"(mu_(s)+tantheta)/(1-mu_(s) tantheta))^(1//2)=((300xx9.8xx(0.2+tan15^@))/(1-(0.2xxtan15^@)))^(1//2)`
`=((2940xx(0.4679))/(0.9464))^(1//2)=(1453.535)^(1//2)`
`v_(max)=38.1ms^(-1)`