name 2 particles which do not exert gravitational force on each other
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When two bodies of masses m₁ and m₂ are placed at a distance r, the Gravitational force exerted by the particles on each other is given by:
where G is the Universal Gravitational constant.
Now, the Force will be zero if one of the masses is zero. If you take one particle having no rest mass, such as gamma radiations, then the gravitational force will be zero (because gamma radiations do not have any particles within it, so it has no rest mass). The other particle may be anything (of course except your skin, because gamma radiations are harmful as they have high penetrating power).
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