Question

The $ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}$. $I_{BC}$ and $I_{CA}$ are the moments of inertia of the plate about $AB,BC$ and $CA$ respectively. Which one of the following relations is correct?

• A. $I_{AB}+I_{BC}=I_{CA}$
• B. $I_{CA}$ is maximum
• C. $I_{AB}>I_{BC}$
• D. $I_{BC}>I_{AB}$

Answer 1

Answer: (D)

The intersection of medians is the centre of mass of the triangle. Since the distances of centre of mass from the sides is related as $x_{BC}<x_{AB}<x_{AC}$.
Therefore $I_{BC}>I_{AB}>I_{AC}$
or $I_{BC}>I_{AB}$.