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. (`i`),(`ii`)
B. (`ii`),(`iii`)
C. (`ii`),(`iv`)
D. (`i`),(`ii`),(`iii`)

Explanation

`I_(x)=I_(y)=(mL^(2))/(12)xx2+{0+m((L)/(2))^(2)}xx2`
`=(mL^(2))/(6)+(mL^(2))/(2)=(2)/(3)mL^(2)`
`I_(z)=I_(x)+I_(y)=(4)/(3)mL^(2)`
`I_(side)=0+(mL^(2))/(3)xx2+(0+mL^(2))=(5)/(3)mL^(2)`
`I_(corn er)=(I_(z))_(c.m)+4m((L)/(sqrt2))^(2)`
`=(4)/(3)mL^(2)+2mL^(2)=(10)/(3)mL^(2)`