question_answer

There is a flat uniform triangular A plate ABC such that \[AB=4cm,\text{ }BC=3cm\]and angle\[abc=90{}^\circ \]. The moment of inertia of the plate about AB, BC and CA as axis is respectively \[{{I}_{1,}}{{I}_{2}}\]and\[{{I}_{3}}\]. Which one of the following is true?     

A) \[{{I}_{3}}>{{I}_{2}}\]

B) \[{{I}_{2}}>{{I}_{1}}\]

C) \[{{I}_{3}}>{{I}_{1}}\]

D) \[{{I}_{1}}>{{I}_{2}}\]

Correct Answer: B

Solution :

[b] Moment of Inertia depend upon mass and     distribution of masses as I\[=\Sigma m{{r}^{2}}.\] Further, as the distance of masses is more, more is the moment of Inertia. If we choose BC as axis. Distance is maximum. Hence, Moment of Inertia is maximum. \[\therefore \,\,{{I}_{2}}>{{I}_{1,}}{{I}_{2}}>{{I}_{3}}\]