Maths JEE Main Full Syllabus Mock Test 75 Question New Syllabus. TEST 5 PCM Numeric Response
Published on: August 14, 2026

A thin square plate has mass and side . Four holes, each of radius , are cut out as shown in following figure. The ratio of moment of inertia of the remaining portion to the moment of inertia of the complete place is

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The correct answer is:
0.26

(0.26) According to the figure, mass per unit area of the plate,

But mass of each hole,

Since

Distance of the centre of a hole and centre of the plate

Using parallel axes theorem, the moment of inertia of a hole about the axis,

Moment of inertia of four holes about the -axis

Moment of inertia of the complete square plate,

Therefore, moment of inertia of the remaining portion about the -axis,

The required ratio

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