Question

FIND THE CENTER OF MASS OF A UNIFORM PLATE HAVING SEMICIRCULAR INNER AND OUTER BOUNDARIES OF RADII R1 AND R2 FROM THE CENTRE O

Answer 1

Here is your answer:

Centre of mass will be at :

==>  [(πR₂²/2)(4R₂/3π) - (πR₁²/2)(4R₁/3π)] / [(πR₂²/2) - (πR₁²/2)]

==>  [(2/3)R₂³ - (2/3)R₁³] / [π/ 2(R₂² - R₁²)]

==>  [4(R₂-R₁)(R₂² + R₁² + R₁R₂)] / [3π(R₂-R₁)(R₂+R₁)]

==>  [4(R₂² + R₁² + R₁R₂)] / [3π (R₁ + R₂)] 

==> [4(R₂² + R₁² + R₁R₂)] / [3π (R₁ + R₂)] above the centre.

Hope this helps you

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