Question

Four point masses, each of mass m are connected at corners of a square of side 'a' by massless rods as shown in the figure. x and y axes are in the plane of the system and z axis is perpendicular to the plane and passing through the center of the square. Then,

• A. Moment of inertia of the system about x axis is $I_x=m{a}^2$
• B. Moment of inertia of the system about y axis is $I_y=m{a}^2$
• C. Moment of inertia of the system about the diagonal axis AA' is $I_{A{A}^{\prime }}=m{a}^2$
• D. Moment of inertia of the system about z axis is $I_{z^{\prime }}=m{a}^2$

Answer 1

Answer: (A), (B), (C)

Moment of inertia of the system about the diagonal axis AA' is $I_{A{A}^{\prime }}=m{a}^2$
Moment of inertia of the system about y axis is $I_y=m{a}^2$
Moment of inertia of the system about x axis is $I_x=m{a}^2$

$I_{xx}=m{\left(\frac{a}{2}\right)}^2+m{\left(\frac{a}{2}\right)}^2+m{\left(\frac{a}{2}\right)}^2+m{\left(\frac{a}{2}\right)}^2=m{a}^2$
$I_{yy}=m{\left(\frac{a}{2}\right)}^2+m{\left(\frac{a}{2}\right)}^2+m{\left(\frac{a}{2}\right)}^2+m{\left(\frac{a}{2}\right)}^2=m{a}^2$
$I_{A{A}^{\prime }}=m{\left(\frac{a}{\sqrt{2}}\right)}^2+m{\left(\frac{a}{\sqrt{2}}\right)}^2+0+0=m{a}^2$
$I_{zz}=\left(m{\left(\frac{a}{\sqrt{2}}\right)}^2\right)\times 4=2m{a}^2$