question_answer

Four point masses, each of value m, are placed at the corners of a square ABCD of side \[l\]. The moment of inertia of this system about an axis passing through A and parallel to BD is     AIEEE  Solved  Paper-2006

A) \[2m{{l}^{2}}\]                 

B) \[\sqrt{3}\,m{{l}^{2}}\]

C)                        \[3\,m{{l}^{2}}\]              

D)        \[\,m{{l}^{2}}\]

Correct Answer: C

Solution :

The situation is shown in figure. \[{{l}_{BD}}=m\times D{{P}^{2}}+m\times B{{Q}^{2}}+m\times C{{A}^{2}}\] \[=2\times m\times {{\left( \frac{\sqrt{2}l}{2} \right)}^{2}}+m\times {{(\sqrt{2}l)}^{2}}=3m{{l}^{2}}\]