A circular racetrack of radius 100 m is blanked at an angle of `45 ^(@)` . What is the
(i) Optimum speed of race car to acoid wear and tear of its tyres ?
(ii) Maximum permissible speed to acoid slipping if the coefficient of friction is `0*22` ?

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