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

Answer

A, B, C

Explanation

Road has a length =L
It makes an angle e`theta` wilth the floor.
The vertical wall has a height =h

`R_2=mg-R_1costheta`………….1
`R_1sintheta=muR_2`…….2
`R_1costhetaxx(h/(tantheta)+R_1sinthetaxxh`
`=mgxxL/2costheta`
`rarr R_1=(mgxxL/2costheta)/({(cos^2theta)/(sintheta)h+sinthetah})`
`rarr R_1costheta=(1/2mgLcos^2theta)/({(cos^2theta)/(sintheta)h+sinthetaxxh})`
`rarr mu=(R_1sintheta)/R_2`
`=(R_1sintheta)/(mg-R_1costheta)`
`-. mu=(L/2costhet.sinthetaxx2sintheta)/(2(cos^2thetah+sin^2theta)h=Lcos^2thetasintheta)`
`rarr mu=(Lcosthetains^2theta)/(2h-Lcos^2thetasintheta)`