Question

Three thin uniform rods each of mass M and length L are placed along the three axis of a cartesian coordinate system with one end of each rod at the origin. The M.I. of the system about z-axis is-

• A. $\frac{M{L}^2}{3}$
• B. $\frac{2M{L}^2}{3}$
• C. $\frac{M{L}^2}{6}$
• D. $M{L}^2$

Answer 1

The correct option is B $\frac{2M{L}^2}{3}$

REF.Image.

Solution

Total $I=I_x+I_y+I_z$

$I_x=\frac{M{L}^2}{3}$ [MI of rod about end]

similarly

$I_y=\frac{M{L}^2}{3}$

$I_z=0$ as the rod is lie in the

2-axis which is the axis of ratio

so, $I_{Total}=\frac{M{L}^2}{3}+\frac{M{L}^2}{3}+0=\frac{2M{L}^2}{3}$

option - B is correct.