A uniform solid disk rolling down an incline making angle `theta` with the horizontal. The minimum coefficient of friction required to maintain pure rolling motion for the disk is.

Options

A. `((2)/(3) tan theta)`
B. `((1)/(3) tan theta)`
C. `((2)/(5) tan theta)`
D. `((1)/(2) tan theta)`

Answer

D

Explanation

(d) Torque about the `CM` is caused by friction because the lever arm of the weight force is zero :
`tau = fR = I prop`
`f = mu n = mu m g cos theta`
`mu = (f)/(mg cos theta) =(I prop//R)/(mg cos theta)`
=`(((2)/(3) g sin theta)((1)/(2) mR^2))/(R^2 mg cos theta) =((1)/(2) tan theta)`
As there is no slipping between any point of contact hence distance moved by the man `2 L`.