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

We know that maximum permissible speed on a banked road to avoid slipping is ,
`v_("max")=[(rg(mu_(s)+tantheta))/(1-mu_(s)tantheta)]^(1//2)`
Now,putting the values given in the question,
`r=300m,theta=15^(@),g=9.8(~~10)ms^(-2)"and "mu_(s)=0.2`
We obtion, `v_("max")=[(300xx9.8(0.2+tan15^(@)))/(1-0.2tantheta15^(@))]^(1//2)`
`=[(300xx9.8(0.2+0.26))/(1-0.2xx0.26)]^(1//2)`
After solve this, we get, `v_("max")=38.1ms^(-1)`