Question

Two particles each of mass $m$, and other particle of mass $2 m$ are situated at the vertices of an equilateral triangle ABC of side $L$. What is the moment of inertia of the system about the line XY perpendicular to $AB$ in the plane of $ABC$ ?

• A. $\frac{3}{2} mL ^{2}$
• B. $2 mL ^{2}$
• C. $\frac{5}{4} mL ^{2}$
• D. Moment of Inertia of the system

Answer 1

Answer: (A)

Moment of inertia of the system
$I =I_{A}+I_{B}+I_{C}=0+m L^{2}+2 m \times\left(\frac{L}{2}\right)^{2} $
$=m L^{2}+\frac{2 m L^{2}}{4}$
$=m L^{2}+\frac{m L^{2}}{2}$
$=\frac{3}{2} m L^{2}$