Three thin uniform rods each of mass M and length L are placed along the three axes of a cartesian coordinate system. The moment of inertia of the system about z-axis is

Options

A. `(ml^(2))/(3)`
B. `(2ML^2)/(3)`
C. `(ML^(2))/(6)`
D. `ML^(2)`

Answer

B

Explanation

The moment of inertia of a thin rod of mass M and length L about an axis passing through one end of the rod and perpendicular to the length of the rod is `(1)/(3) ML^(2)` . Moment of inertia of the rod about z-axis is zero .
Therefore , moment of inertia of the system about the z-axis = `(1)/(3) ML^(2) + (1)/(3) ML^(2) + 0 = (2)/(3) ML^(2)`