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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

A hemispherical cavity of radius R is created in a solid sphere of radius 2 R as shown in the figure. The y -coordinate of the centre of mass of the remaining sphere is

Options

  1. Ay CM = - R 15
  2. By CM = - R 4 0
  3. Cy CM = - R 30
  4. Dy CM = - R 20

Correct answer

B. y CM = - R 4 0

Step-by-step solution

x CM = 4 3 π 2 R 3 0 - 2 3 π R 3 R 4 3 π 2 R 3 - 2 3 π R 3 = - R 1 5 y CM = 4 3 π 2 R 3 0 - 2 3 π R 3 3 R 8 4 3 π 2 R 3 - 2 3 π R 3 = - R 4 0 z CM = 0

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