Question

Three thin rods, each of length $2$m and mass $3$ kg are placed along x, y and z axes, such that one end of each rod is at the origin. The moment of inertia of this system about the z axis is?

• A. $2$ kg $m^2$
• B. $4$ kg $m^2$
• C. $6$ kg $m^2$
• D. $8$ kg $m^2$

Answer 1

The correct option is D $8$ kg $m^2$

Using perpendicular axis theorem

$I_z=I_x+I_y$

$I_z=\frac{1}{3}{ML}^2+\frac{1}{3}{ML}^2$

$=\frac{1}{3}(3\times 2\times 2)+\frac{1}{3}(3\times 2\times 2)$

$=4+4=8Kg{m}^2$