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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

Two solid hemispheres of radii R and R 2 with centers O and O ′ respectively as shown in figure. The density of bigger hemisphere is ρ and that of smaller hemisphere is 2 ρ . Taking center of bigger hemisphere is at origin and the distance between centers of two hemispheres O O ′ is R 10 find co-ordinates of center of mass of the system.

Options

  1. A- R 50 , 21 R 80
  2. B- R 30 , 21 R 80
  3. C- R 50 , 7 R 16
  4. D- R 30 , 7 R 16

Correct answer

A. - R 50 , 21 R 80

Step-by-step solution

Let, M 2 = M , M 1 = 4 M x c m = 4 M O - M R 10 4 M + M ⇒   x cm = - R 50 y c m = 4 M 3 R 8 - M R 16 4 M + M ⇒   y cm = 21 R 80

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