Question

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

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

Answer 1

The correct option is B $I_{BC}>I_{AB}$

Moment of inertia of a body$=\int \delta m{r}^{2}dr$

Hence the object which have most distant mass in the body has maximum moment of inertia.

Maximum distance of a point from AB=3.

Maximum distance of a point from BC=4.

Maximum distance of a point from AC<3

$⟹I_{BC}>I_{AB}>I_{AC}$