Three particles, each of mass grams situated at the vertices of an equilateral of side cm (as shown in the figure). The moment of inertia of the system about a line perpendicular to and in the plane of in -cm² units will be:
1
2 ma2
2
3/2 ma2
3
3/4 ma2
4
5/4 ma2
Official Solution
Correct Option:
(4)
Given: Three particles of mass m grams each are placed at the vertices of an equilateral triangle ABC with side length a cm.
Required: Find the moment of inertia of the system about the line AX, which is:
Perpendicular to side AB
Lies in the plane of triangle
Coordinate Geometry Setup:
Let point
Then
Point lies above the midpoint of , so: Midpoint of Height of equilateral triangle = So
Moment of Inertia Calculation:
About point A: Distance = 0 →
Point B: Perpendicular distance from AX = →
Point C: Perpendicular distance from AX = →
Total Moment of Inertia:
Final Answer:
About Moment Of Inertia - WBJEE
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