A cylinder of mass `5 kg` and radius `30 cm` is rolling down an inclined plane at an angle of `45^(@)` with the horizontal. Calculate (i) force of friction (ii) acceleration of cylinder (iii) minimum value of coeff. of static friction so that cylinder does not slip while rolling down the plane.

Explanation

Here, `m = 5 kg, r = 30 cm = 0.3m, theta = 54^(@)`
(i) Force of friction,
`f = (1)/(3)mg sin theta = (1)/(3) xx 5 xx 9.8 xx (1)/(sqrt(2)) = 11.55N`
(ii) acceleration, `a = (2)/(3)g sin theta = (2)/(3) xx 9.8 xx (1)/(sqrt(2))`
`=4.62 m//s^(2)`
(iii) Minimum value of coeff. of friction
`mu_(s) = (1)/(3) tan theta = (1)/(3)tan 45^(@) = (1)/(3)`