System of Particles and Rotational Motion - Result Question 65
72. $ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I _{A B}, I _{B C}$ and $I _{C A}$ are the moments of inertia of the plate about $A B, B C$ and $C A$ as axes respectively. Which one of the following relations is correct?
[1995]
(a) $I _{A B}>I _{B C}$
(b) $I _{B C}>I _{A B}$
(c) $I _{A B}+I _{B C}=I _{C A}$
(d) $I _{CA}$ ismaximum
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Answer:
Correct Answer: 72. (b)
Solution:
- (b) Since distances of centre of mass from the sides are related as : $x _{B C}>x _{A B}>x _{A C}$, therefore, $I _{B C}>I _{A B}>I _{A C}$ or $I _{B C}>I _{A B}$.
The intersection of medians is the centre of mass of the triangle.
