Question

Moment of inertia of uniform triangular plate about axis passing through sides $AB$, $AC,BC$ are $I_P,I_B$ and $I_H$ respectively and about an axis perpendicular to the plane and passing through point $C$ is $I_C$ Then:

• A. $I_C>I_P>I_B>I_H$
• B. $I_H>I_B>I_C>I_P$
• C. $I_P>I_H>I_B>I_C$
• D. none of these

Answer 1

Answer: (A)

Moment of inertia is more when mass is farther from the axis. In case of axis $BC$, mass distribution is closest to it and in case of axis $AB$ mass distribution is farthest. Hence
$I_{BC}<I_{AC}<I_{AB}\Rightarrow I_P>I_B>I_H$
$I_C=I_{CM}+m{y}^2=I_B^{\prime }-m{x}^2+m{y}^2$
Here $I_B^{\prime }$ is moment of inertia of the plate about an axis perpendicular to it and passing through $B$.
$\Rightarrow I_C=I_B^{\prime }+m\left(y^2-x^2\right)=I_P+I_B+m\left(y^2-x^2\right)$
It means $I_C>I_P+I_B$ also $I_C>I_P$
$\therefore I_C>I_P>I_B>I_H$