Question

The moment of inertia of a disc of mass $M$ and radius $R$ about an axis, which is tangential to the circumference of the disc and parallel to its diameter is

• A. $\frac{3}{2}MR^2$
• B. $\frac{2}{3}MR^2$
• C. $\frac{5}{4}MR^2$
• D. $\frac {4}{5}MR^2$

Answer 1

Answer: (C)

$\frac{5}{4}MR^2$

Answer 2

The moment of inertia of a disc about its diameter (i.e. $z$ axis) is $I_{0}=\frac{MR^{2}}{4}$ $\therefore$ According to parallel axis theorem, moment of inertia about the required axis (i.e. z' axis) is $I=I_{0}+MR^{2}$ $=\frac{MR^{2}}{4}+MR^{2}=\frac{5MR^{2}}{4}$