First slide

Universal law of gravitation

Question

Three equal masses m are placed at the three vertices of an equilateral triangle of side a.The gravitational force exerted by this system on another particle of mass m placed at the midpoint of a side

Easy

A

$\large \frac {Gm^2}{3a^2}$
B

$\large \frac {4Gm^2}{3a^2}$
C

$\large \frac {Gm^2}{a^2}$
D

$\large \frac {Gm^2}{2a^2}$

Solution

$\large F=\frac {G(m)^2}{(a/2)^2}-\frac {G(m)^2}{(a/2)^2}+\frac {G(m)^2}{(\sqrt 3/2)^2}$
$\large F=\frac {4Gm^2}{3a^2}$

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