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Four identical uniform rods of mass M=6k...


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-

A

`(5)/(7)`

B

`(5)/(12sqrt(3))`

C

`(5sqrt(3))/(7)`

D

`(7)/(5sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
B
`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))`
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