A uniform rod of length `L` rests against a smooth roller as shown in Fig. Find the friction coefficient between the ground and the lower end if the minimum angle that the rod can make with the horizontal is `theta`.

Options

A. `mu = (l" cos "0" sin"^(2)0)/(2h-l "cos"^(2)0"sin"0)`
B. `mu=(l"sin"0"cos"^(2)0)/(2h-l"cos"0"sin"^(2)0)`
C. `mu=(l"sin"0"cos"^(2)0)/(2h-l"cos"0"sin"0)`
D. None of these

Answer

A

Explanation

`SigmaF_(x) muN_(2)-N_(1) "sin"0=0`
`SigmaF_(y)=N_(1)"cos"0+N_(2)=mg=0`
`Sigmatau=0` about point A
`N_(1) xx(h)/("sin"0) ="mg" xx (e)/(2) cos0`
By solving
`mu = (e"cos" 0 "sin"^(2)0)/(2h-e "cos"^(2)0"sin"0)`