Question

Four identical rods each of mass $m$ and length $\ell $ make a square frame in $xy$ plane as shown. Calculate its moment of inertia about the $x$ -axis:-

• A. $\frac{5}{3}m\ell ^{2}$
• B. $\frac{4}{3}m\ell ^{2}$
• C. $m\ell ^{2}$
• D. None of these

Answer 1

Answer: (A)

$I=I_{1}+I_{2}+I_{3}+I_{4}$
$=\frac{m L^{2}}{3}+\left(0 + m L^{2}\right)+\frac{m L^{2}}{3}+0$
$I=\frac{5}{3}mL^{2}$