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By accepting a equation of friction forc...

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.

Text Solution

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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)`
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