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99 Percentile Qs Bank for JEE MainPhysicsCenter of Mass, Momentum and Collision

A system consists of three particles each of mass ' m ₁ ' placed at the corners of an equilateral triangle of side ' L 3 , A particle of mass ' m ₂ ' is placed at the mid point of any one side of the triangle. Due to the system of particles, the force acting on m ₂ is

Options

  1. A3 Gm ₁ ~m ₂ ~L ^2
  2. B6 Gm ₁ ~m ₂ ~L ^2
  3. C9 Gm ₁ ~m ₂ ~L ^2
  4. D12 Gm ₁ ~m ₂ ~L ^2

Correct answer

D. 12 Gm ₁ ~m ₂ ~L ^2

Step-by-step solution

From the fig., we can see that the forces due to masses at Q and R cancel each other as they are equal and opposite. The force at P is only due to m ₁ . In P Q S , h = L 3 30^ = L 3 6 Force on m ₂ due to m ₁ at P is aligned F & = G m₁ m₂ ( L 3 6 )^2 & = G m₁ m₂ 12 L^2 & = 12 Gm ₁ ~m ₂ ~L ^2 aligned

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