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MHT CET20239 May 2023Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A thin rod of length ' L ' is bent in the form of a circle. Its mass is ' M '. What force will act on mass ' m ' placed at the centre of this circle? ( G = constant of gravitation)

Options

  1. Azero
  2. BGMm 4 ~L ^2 ^2
  3. C4 ^2 GMm L
  4. D2 GMm L ^2

Correct answer

A. zero

Step-by-step solution

Consider two diametrically and equal small and equal mass segments dM ₁ and dM ₂ Force at the centre due to dM ₁ is F ₁= GmdM ₁ r ^2 Similarly, Force at the centre due to dM ₂ is F ₂= GmdM ₂ r ^2 But F ₁=- F ₂ F ₁+ F ₂=0 ( the forces cancel each other out as they are equal and opposite) If this process is done for all such dM segments, we find the net force at the centre of the circle to be zero.

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