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JEE Main 202329 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
29 January
Shift
Morning Shift
Subject
Physics
Chapter
Gravitation

JEE Main 2023 · 29 January · Morning Shift · Physics · Gravitation

Two particles of equal mass m move in a circle of radius r under...

Two particles of equal mass mm move in a circle of radius rr under the action of their mutual gravitational attraction. The speed of each particle will be :Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational attraction.

Options

  1. AGm2r\sqrt{\dfrac{Gm}{2r}}
  2. B4Gmr\sqrt{\dfrac{4Gm}{r}}
  3. CGmr\sqrt{\dfrac{Gm}{r}}
  4. DGm4r\sqrt{\dfrac{Gm}{4r}}

Correct answer

D. Gm4r\sqrt{\dfrac{Gm}{4r}}

Step-by-step solution

Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational attraction.

Let speed of both the particles be vv.

Then, gravitational force between the particles will provide the required centripetal force.

Therefore,

G(m)(m)(2r)2=mv2r\dfrac{G\left(m\right)\left(m\right)}{{\left(2r\right)}^{2}} = \dfrac{m{v}^{2}}{r}

⇒v=Gm4r⇒ v = \sqrt{\dfrac{Gm}{4r}}

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