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JEE Main20211 Sep 2021Evening ShiftPhysicsGravitationActual

Four particles each of mass M , move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is :

Options

  1. A1 2 G M R 2 2 + 1
  2. B1 2 G M R ( 2 2 + 1 )
  3. C1 2 G M R 2 2 - 1
  4. DG M R

Correct answer

A. 1 2 G M R 2 2 + 1

Step-by-step solution

. F net  = F 1 + 2   F 2 cos 45 ° = G M 2 ( 2 R ) 2 + 2 × G M 2 ( 2 R ) 2 × 1 2 = G M 2 4 R 2 + G M 2 2 R 2 = ( 4 + 2 ) G M 2 4 2 R 2 Now F C = F net  M V 2 R = ( 4 + 2 ) G M 2 4 2 R 2 V = ( 4 + 2 ) 4 2 G M R

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