A system consists of three particles each of mass ' m₁ ' placed at the corners of an equilateral triangle of side ' L/3 ', A particle of mass ' m₂ ' is placed at the mid point of any one side of the triangle. Due to the system of particles, the force acting on m₂ is (a) 3Gm₁ m₂L² (b) 6Gm₁ m₂L² (c) 9Gm₁ m₂L² (d) 12Gm₁ m₂L²

Answer: (d). The two masses at the ends of the side pull m₂ equally in opposite directions, so they cancel. Only the opposite vertex acts, at distance equal to the height h = √(3)/2 · L/3 = (√(3)L)/(6). h² = (3L²)/(36) = L²/12 F = (Gm₁m₂)/(h²) = (12Gm₁m₂)/(L²) So the answer is (d).

A system consists of three particles each of mass ' m₁ ' placed at… | MHT CET 2023 (10 May, Shift 2)

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Newton's Law of Gravitation

A system consists of three particles each of mass ' $m_1$ ' placed at the corners of an equilateral triangle of side ' $\frac{L}{3}$ ', A particle of mass ' $m_2$ ' is placed at the mid point of any one side of the triangle. Due to the system of particles, the force acting on $m_2$ is

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Answer: (d)

The two masses at the ends of the side pull $m_2$ equally in opposite directions, so they cancel.
Only the opposite vertex acts, at distance equal to the height $h = \frac{\sqrt{3}}{2} \cdot \frac{L}{3} = \frac{\sqrt{3}L}{6}$ .
$h^2 = \frac{3L^2}{36} = \frac{L^2}{12}$
$F = \frac{Gm_1m_2}{h^2} = \frac{12Gm_1m_2}{L^2}$
So the answer is (d).

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