Question

Four point masses, each of mass $m$ are arranged in $X-Y$ plane as shown. Find the moment of inertia about $X$-axis.

• A. $3ma^2$
• B. $5ma^2$
• C. $4ma^2$
• D. $6ma^2$

Hint:

Shortcut: For X-axis → only y-coordinates matter Ignore masses lying on X-axis (they contribute zero)

Answer 1

The Correct Option is B

Concept: Moment of inertia about $X$-axis for point masses: \[ I = \sum m y^2 \] (where $y$ = perpendicular distance from $X$-axis)

Step 1: Identify coordinates of masses
From diagram:
• Mass at $(0,0)$ → $y = 0$
• Mass at $(a, a)$ → $y = a$
• Mass at $(a, -2a)$ → $y = -2a$
• Mass at $(3a, 0)$ → $y = 0$

Step 2: Calculate moment of inertia
\[ I = m(0)^2 + m(a)^2 + m(-2a)^2 + m(0)^2 \] \[ I = 0 + ma^2 + 4ma^2 + 0 \] \[ I = 5ma^2 \] Final Answer: Option (B)