A massless spool of inner radius `r` outer radius `R` is placed against a vertical wall and a titled split floor as shown. A light inextensible thread is tightly wound around the spool through which a mass `m` is hainging. There exists no friction at point `A`, while the coefficient of friction between the spool and point `B` is `mu`. The angle between the two surface is `theta`

Options

A. The magnitude of force on the spool at B in order ot maintain equilibrium is mg` sqrt(((r )/( R))^(2)+(1-( r)/( R))^(2)(1)/(tan^(2)theta))`
B. The magnitude of force on the spool at B in order to maintain equilibrium is mg `(1-(r )/( R))(1)/( tan ^(2) theta)`
C. The minimum value of `mu` for the system to ramain in equilibrium is `( cot theta)/((R//r)-1)`
D. The minimum value of `mu` for the system to ramain in equilibrium is `( tan theta)/((R//r)-1)`

Answer

A, D