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99 Percentile Qs Bank for JEE MainPhysicsMotion in Two Dimensions

A body of mass ' m ' is moving with speed ' V ' along a circular path of radius ' r '. Now the speed is reduced to V 2 and radius is increased to ' 3 r '. For this change, initial centripetal force needs to be

Options

  1. Aincreased by 7 12 times.
  2. Bincreased by 10 12 times.
  3. Cincreased by 11 12 times.
  4. Dincreased by 1 12 times.

Correct answer

C. increased by 11 12 times.

Step-by-step solution

aligned & Centripetal force, F = mv ^2 r & F ₁= mv ₁^2 r ₁ and F ₂= mv ₂^2 r ₂ & F ₂ ~F ₁ = v ₂^2 v ₁^2 r ₁ r ₂ & v ₂= v ₁ 2 and r ₂=3 r ₁ & F ₂ ~F ₁ = ( 1 2 )^2 1 3 = 1 12 & v ₂= v ₁ 2 and r ₂=3 r ₁ & F ₂ ~F ₁ = ( 1 2 )^2 1 3 = 1 12 & ~F ₂= F ₁ 12 aligned Change in force =F₂-F₁= F₁ 12 -F₁=- 11 12 F₁ Hence force is decreased by 11 12 times.

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