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)/(2)`
B. `sqrt((3)/(2)L)`
C. `(L)/(sqrt2)`
D. `(L)/(sqrt3)`

Explanation

`I_(A)=(mL^(2))/(3)xx2+[(mL^(2))/(12)+m((sqrt3L)/(2))^(2)]=(3)/(2)mL^(2)`
`I_(A)=3 mk^(2)`
`(3mL^(2))/(2)=3 mL^(2)implies k=(L)/(sqrt2)`