Two particles of equal mass 'm' move in a circle of radius… — JEE Main 2023 Physics PYQ

JEE Main 2023 · 29 Jan · Shift 1

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

A.
$\sqrt{\dfrac{Gm}{r}}$
B.
$\sqrt{\dfrac{Gm}{2r}}$
C.
$\sqrt{\dfrac{4Gm}{r}}$
D.
$\sqrt{\dfrac{Gm}{4r}}$

Show answer and solution

Correct option: D

Solution

The two particles move diametrically opposite in the circle, so the distance between them is 2r. The gravitational force provides the centripetal force:

Gm²/(2r)² = mv²/r

Gm²/4r² = mv²/r

v² = Gm/4r

v = √(Gm/4r)

[JEE Main 2023 · 29 Jan · Shift 1]

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