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 ?

Explanation

(a) `v=sqrt(rg tan theta)=sqrt(300xx9.8xxtan 15^(@))=sqrt(300xx9.8xx0.268)=28.1m//s`
(b) `v_("max")=sqrt((gr(mu+tan theta))/((10mu tan theta)))=sqrt((gr(mu_tan 15^(@)))/((1-mu tan 15^(@))))=sqrt((9.8xx300(0.2+0.268))/((1-0.2xx0.268)))=sqrt(1453.85)=38.1m//s`