A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The centre of the smaller circle is at a distance of R/3 from the centre of the larger circle. What is the position of the centre of man of the plate

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Along the line joining the centers and lies at a distance 4R/9 left side, from the center of the hole

Along the line joining the centers and lies at a distance 4R/9 right side, from the center of the hole

Along the line joining the centers and lies at a distance R/9 left side, from the center of the hole

Along the line joining the centers and lies at a distance R/9 right side, from the center of the hole

answer is A.

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Detailed Solution

M=ρ(2R)2π; m=M=ρ(R)2πCMxcm=M(0)−mx2M−m;x2=x=R/3; ∵m=M/4xCm=−x3=−R9 (from the centre of the large disc)i.e. 4R/9 from centre of the hole.

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