Question

A book of mass 0.5 kg has its length 75 cm and breath 25 cm. Then the moment of inertia about an axis perpendicular to the book and passing through centre of gravity of the book is:

• A. $\frac{10}{289}kg-m^2$
• B. $\frac{289}{10}kg-m^2$
• C. $\frac{10}{384}kg-m^2$
• D. $\frac{10}{483}kg-m^2$

Answer 1

The correct option is C $\frac{10}{384}kg-m^2$

$\frac{M{a}^2}{12}+\frac{M{b}^2}{12}$

$\frac{1}{2\times 12}\left\{{\left(\frac{3}{4}\right)}^2++{\left(\frac{1}{4}\right)}^2\right\}$

$\frac{1}{24}\times \frac{10}{16}=\frac{10}{384}kg-m^2$

Hence,

option $\left(C\right)$ is correct answer.