Rotational Motion Question 140
Question: Consider a uniform square plate of side $a$ and mass $M$ . The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its comers is
Options:
A) $\frac{5}{6}Ma^{2}$
B) $\frac{1}{12}Ma^{2}$
C) $\frac{7}{12}Ma^{2}$
D) $\frac{2}{3}Ma^{2}$
Show Answer
Answer:
Correct Answer: D
Solution:
[d] For a rectangular sheet moment of inertia passing through O, perpendicular to the plate is
$I _{O}=M\left( \frac{a^{2}+b^{2}}{12} \right)$
For square plate it is $\frac{Ma^{2}}{6}$$ (as a = b) $
$r=\sqrt{\frac{a^{2}}{4}+\frac{a^{2}}{4}}=\frac{a}{\sqrt{2}}$
$\therefore r^{2}=\frac{a^{2}}{2}$
$\therefore $ Moment of inertia about B parallel to the axis through O is
$I _{B}=I _{O}=Mr^{2}=\frac{Ma^{2}}{6}+\frac{Ma^{2}}{2}=\frac{2Ma^{2}}{6}$ $I=\frac{2}{3}Ma^{2}$
