By accepting a equation of friction force F=mgsintheta{(k^(2))/(k^(2)+R^(2))} derive an expression for the static friction of rolling body from the slope.

By accepting a equation of friction force F=mgsintheta{(k^(2))/(k^(2)+

1.	By accepting a equation of friction force F=mgsintheta{(k^(2))/(k^(2)+R^(2))} derive an expression for the static friction of rolling body from the slope.
Answer» SOLUTION :As shown in figure the normal reaction N nad `mgcostheta` BALANCE each other `therefore N=mgcostheta""......(6)` Taking the ratio of equation (5) and (6) `(F)/(N)=[(K^(2))/(k^(2)+R^(2))]TANTHETA` But `(F)/(N)=mu_(s)` (co-efficient of static friction) `therefore mu_(s)={(k^(2))/(k^(2)+R^(2))}tantheta` `={(1)/(1+(R^(2))/(k^(2)))}tantheta""....(7)`