Four identical uniform rods of mass `M=6kg` each are welded at their ends to form a square and then welded to a uniform ring having mass m=4kg & radius R=1m the system is allowed to roll down on the rough and fixed incline of inclination `theta=30^(@)` (assume no sliding anywhere)
Q. The minimum value of coefficient of friction to prevent slipping is-

Options

A. `(5)/(7)`
B. `(5)/(12sqrt(3))`
C. `(5sqrt(3))/(7)`
D. `(7)/(5sqrt(3))`

Explanation

`I=[(M(Rsqrt(2))^(2))/(12)+M((R)/(sqrt(2)))^(2)]xx4+mR^(2)`
`(4M+m)gsintheta-F=(4M+m)a`
`F.R.=I((a)/(R))`
solving `a=(7g)/(24)`
`F=20alemu(4M+m)gcos30`
`muge(5)/(12sqrt(3))`
`thereforemu_(min)=(5)/(12sqrt(3))`