A circular racetrack of radius 100 m is banked at an angle of `45^(@)`. What is the
(i) Optimum speed of race car to avoid wear and tear of its tyres?
(ii) Maximum permissible speed to avoid slipping if the coefficient of friction is 0.2?

Explanation

At the optimum speed , optimum speed `v_(0)` is given by equation
`v_(0) = (Rg" tan " theta )^(1//2)`
` = (100 xx 9*8 xx tan 45)^(1//2)`
` = 31.3 m//s`
The maximum permissible speed `v_(max)` is given by
`V_(max) = (Rg. (mu_(s) + tan theta )/(1 - mu_(s)tan theta ))^(1//2)`
` = ( 100 xx 9*8 xx (0*2 + tan 45)/(1-0*2 tan 45))^(1//2)`
` = 38.34 ` m/s