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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A thin uniform annular disc of mass M , has an outer radius of 4 R and an inner radius of 3 R as shown in the figure. The work required to take a unit mass from point P on its axis to infinity is

Options

  1. A2 GM 7 R 4 2 - 5
  2. B- 2 G M 7 R ( 4 2 - 5 )
  3. CGM 4 R
  4. D2 GM 5 R 2 - 1

Correct answer

A. 2 GM 7 R 4 2 - 5

Step-by-step solution

W = Δ U = U f - U i = U ∞ - U P = - U P = - m V P = - V P as m = 1 Upon integration, potential at point P will be obtained as given below Let dM be the mass of small ring as shown dM = M π 4 R 2 - π 3 R 2 2 π r dr = 2 Mr dr 7 R 2 dV P = - G d M 1 6 R 2 + r 2 = - 2 GM 7 R 2 ∫ 3 R 4 R r 1 6 R 2 + r 2 dr = - 2 G M 7 R ( 4 2 - 5 ) ∴ W = + 2 GM 7 R 4 2 - 5

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