Three rods each of length L and mass M are placed along X, Y and Z axis in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about Z axis is

Options

A. `(2ML^(2))/(3)`
B. `(4ML^(2))/(3)`
C. `(5ML^(2))/(3)`
D. `(ML^(2))/(3)`

Answer

A

Explanation

M.I. of rod (1) about Z - axis, `I_(1)=(MI^(2))/(3)`
M.I. of rod (2) about Z - axis, `I_(2)=(MI^(2))/(3)`
M.I. of rod (3) about Z - axis, `I_(3)=0`
Because this rod lies on Z - axis
`therefore I_("system")=I_(1)+I_(2)+I_(3)=(2MI^(2))/(3)`.