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. `(2)/(5)ml^(2)`
B. `(4)/(3)ml^(2)`
C. `(2)/(5)ml^(2)`
D. `(3)/(7)ml^(2)`

Answer

A

Explanation

When we rotate the frame about X-axis then two of the rods will rotate about their centres perpendicular to their lengths and the remaining two rods will rotate with their lengths parallel to axis at a distance 1/2. So total moment of inertia of the system can be written as follows:
`I=2(ml^(2))/(12)+2m((l)/(2))^(2)=(ml^(2))/(6)+(ml^(2))/(2)=(2)/(3)ml^(2)`
Hence option (a) is correct.