Three identical rods, each of length `L`, are joined to form a rigid equilateral triangle. Its radius of gyration about an axis passing thorugh a corner and perpendicular to plane of triangle is

Options

A. `l/(sqrt(3))`
B. `l/(sqrt(2))`
C. `l/(sqrt(5))`
D. `l/(sqrt(7))`

Answer

B

Explanation

MI of the system w.r.t an axis `bot ` to plane and passing through one corner
`=(ML^(2))/3+(ML^(2))/3+[(ML^(2))/12+M((sqrt(3)L)/2)^(2)]`
`=(2ML^(2))/3+[(ML^(2))/12+(3ML^(2))/4]`
`=(2ML^(2))/3+(10ML^(2))/12=(3ML^(2))/3=(18 ML^(2))/12=3/2 ML^(2)`
Now, `3/2 ML^(2)=3k^(2)`
`k=l/(sqrt(2))`