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 to maintain equilibrium is `mgsqrt((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 theta)`
C. The minimum value of `mu` for the system to remain in equilibrium is `(cot theta)/((R//r)-1)`
D. the minimum value of `mu` for the system to remain is equilibrium is `(tan theta)/((R//r)-1)`

Answer

A, D

Explanation

`mgr=fR.....(1)`
`N_(1)sin theta+f=mg......(2)`
`N_(1) cos theta+N_(2).....(3)`