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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

Asked in JEE Main 29th Jan 1st Shift 2023 (also AIEEE Re-Scheduled 2011) · Mutual gravitation and binary systems

• (1) √(Gm)/r
• (2) √(Gm)/(4r)
• (3) √(4Gm)/r
• (4) √(Gm)/(2r)

Step-by-step solution

Why the other options are wrong

• (1) Comes from taking the separation of the two particles as r instead of 2r.
• (3) Comes from moving the 4 from the denominator to the numerator while rearranging, which also makes the speed grow with the mutual pull the wrong way.
• (4) Comes from writing the square of the separation as 2r² instead of 4r².

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