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. `10sqrt3 "ms"^(-1)`
B. `9sqrt10 "ms"^(-1)`
C. `sqrt10 "ms"^(-1)`
D. `2sqrt10 "ms"^(-1)`

Answer

B

Explanation

Here, R=300m, `theta=15^(@), g=10ms^(-2), mu=0.2` The optimum speed of the car to avoid wear and tear is given by
`v=sqrt(Rg tan theta)=sqrt(300xx10xxtan 45^(2))=sqrt(810)=9sqrt10ms^(-1)`