Four identical rods each of mass `m` and length `l` are joined to form a rigid square frame. The frame lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its moment of inertial about

Options

A. the x-axis is `(2)/(3)ml^(2)`
B. the z-axis is `(4)/(3)ml^(2)`
C. an axis parallel to the z-axis and passing through a corner is `(10)/(3)ml^(2)`
D. one side is `(5)/(3)ml^(2)`

Explanation

(a). `I_(x)=I_(y)=2[(ml^(2))/(12)+m((l)/(2))^(2)]`
`=(2)/(3)ml^(2)`
(b). `I_(x)=I_(x)+I_(y)=(4)/(3)ml^(2)`
(c). `I=I_(x)+(4m)r^(2)`
`=(4)/(3)ml^(2)+(4m)((l)/(sqrt(2)))^(2)`
`=(10)/(3)ml^(2)`
(d). `I=2(ml^(2))/(3)+ml^(2)=(5)/(3)ml^(2)`