Question

The moment of inertia of a system of two masses $2$ kg and $4$ kg lying in the x-y plane at distances, $2$ m and $4$ m, respectively from the origin about the z-axis is (in $\text{kg m}^2$)

• A. $36$
• B. $48$
• C. $64$
• D. $72$
• E. $80$

Hint:

For point masses: - Always use $I = mr^2$ - Add contributions of all masses

Answer 1

The Correct Option is D

Concept: Moment of inertia about an axis is given by: \[ I = \sum m r^2 \] where $r$ is the perpendicular distance from the axis.

Step 1: Write contributions of each mass.
For $2$ kg at $2$ m: \[ I_1 = 2 \times (2)^2 = 2 \times 4 = 8 \] For $4$ kg at $4$ m: \[ I_2 = 4 \times (4)^2 = 4 \times 16 = 64 \]

Step 2: Find total moment of inertia.
\[ I = I_1 + I_2 = 8 + 64 = 72 \]