A circular racetrack of radius 300 m is banked at an angle of `15^(@)` The coefficient of friction between the wheels of a race car and the road is 0.2. The optimum speed of the race car to avoid wear and tear on its tyres is

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)`