One end of a heavy uniform rod AB can slide along rough horizontal guiding surface CD with the help of massless ring as shown in the figure. The dimension of ring is negligible. BE is the ideal string if `angleEBA` is right angle and `alpha` is the angle between rod AB and horizontal when the rod is on the verge of sliding. Find the coefficient of friction between ring and horizontal guiding surface CD.

Options

A. `(tanalpha)/(2+tan^(2)alpha)`
B. `(tanalpha)/(1+2tan^(2)alpha)`
C. `(tanalpha)/(2-tanalpha)`
D. `(tanalpha)/(1-tan^(2)alpha)`

Answer

B

Explanation

Since body is in equilibrium under the influence of three forces only so they must e concurrent. Using Lami's theorem we can write
`tanalpha=(L)/(2x)` and `tan(alpha+lamda)=(L)/(x)`
`tan(alpha+lamda)=2tanalphaimplies(tanalpha+tanlamda)/(1-tanalphatanlamda)=2tanalpha`
`impliestanalpha+tanlamda=2tanalpha-2tan^(2)alphatanlamda`
`impliestanlamda=mu=(tanalpha)/(1+2tan^(2)alpha)`