Question

A square metallic sheet of side $l$ is cut diagonally to form a triangle. If the mass of the triangular sheet is $M$, what is its moment of inertia about the diagonal.

• A. $\frac{M{l}^2}{18}$
• B. $\frac{M{l}^2}{12}$
• C. $\frac{M{l}^2}{6}$
• D. $\frac{M{l}^2}{3}$

Answer 1

The correct option is B $\frac{M{l}^2}{12}$

Given: A square metallic sheet of side l is cut diagonally to form a triangle. If the mass of the triangular sheet is M,

To find the moment of inertia of the square sheet about the diagonal.

Solution:

Since diagonals of a square are at right angles so due to symmetry you can use perpendicular axis theorem

We get

$I_z=I_{x{x}^{\prime }}+I_{y{y}^{\prime }}⟹\frac{M{l}^2}{6}=2\times Ix{x}^{\prime }$

(as the diagonals are symmetric)

$I_{x{x}^{\prime }}=\frac{M{L}^2}{12}$

is the the moment of inertia of the square sheet about the diagonal.