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Plz...plz sir reply this question as soon as possible. It is from RD Sharma.Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii R1 and R2 (for detail see fig)

Kaushki , 6 Years ago
Grade 12th pass
anser 1 Answers
Arun

Last Activity: 6 Years ago

Centre of mass of the plate will be on symmetrical axis.
Centre of mass at y 
= [(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.

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