Four identical rods of mass `M = 6 kg` each are welded at their ends to form a square and then welded to a massive ring having mass `m = 4 kg` and radius `R = 1m`. If the system is allowed to roll down the incline of inclination `theta = 30^@`, determine the minimum value of the coefficient of static friction that will prevent slipping.

The moment of inertia of the system about the centre of ring will be

Options

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

Answer

B

Explanation

`i=[(M(Rsqrt(2))^(2))/(12)+M((R)/(sqrt(2)))^(2)]xx4+mR^(2)`
`=20kgm^(2)`.
`(4M+m)g sin theta -F=(4M+m)a.`
`F.R.=I((a)/(R))`
Solving
`a=(7g)/(24)`
`F=20alemu(4M+m)g cos 30`
`muge(5)/(12sqrt(3))`
`:. mu _(m i n)=(5)/(12sqrt(3))`