First slide

Moment of intertia

Question

ABC is right angled triangular plane of uniform thickness. The sides are such that AB > BC as shown in figure. I_1, I₂, I₃ are moments of inertia about AB, BC and AC, respectively. Then, which of the following relations is correct? UIPMER 2017]

Moderate

A

$I_{1} = I_{2} = I_{3}$
B

$I_{2} > I_{1} > I_{3}$
C

$I_{3} < I_{2} < I_{1}$
D

$I_{3} > I_{1} > I_{2}$

Solution

The moment of inertia of a body about an axis depends not only on the mass of the body but also on the distribution of mass about the axis. For a given body, mass is same, so it will depend only on the distribution of mass about the axis. The mass is farthest from axis BC, so I₂ is maximum, mass is nearest to axis AC, so I₃ is minimum.
Hence, the correct sequence will be $I_{2} > I_{1} > I_{3}$

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