Question

Three particles, each of mass m are situated at the vertices of an equilateral triangle ABC of side L figure. Find thee moment of inertia of the system about the line AX perpendicular to AB in the plane of ABC

A. `(5)/(4)ml^(2)`
B. `(3)/(2)ml^(2)`
C. `(3)/(4)ml^(2)`
D. `2 ml^(2)`

Answer 1

Correct Answer - A
From Fig.
`sin 30^(@) = (CN)/(CA) = (CN)/(l)`
`CN = l sin 30^(@) = (l)/(2)`
`I = m_(A) (0)^(2) + m_(B) (l)^(2) + m_(C) (CN)^(2)`
`+ 0 + ml^(2) + m(l//2)^(2) = (5)/(4)ml^(2)`