Physics

Physics

Problem

Two identical spheres, each of mass 2 kg2\,\text{kg}, are kept 0.40 m0.40\,\text{m} apart and attract each other with a force FF. Each sphere is replaced by one of mass 6 kg6\,\text{kg} and the distance between their centres is increased to 0.80 m0.80\,\text{m}. Calculate the new gravitational force between the spheres in terms of FF.
Intuitive explanation

Gravitational force depends on both the masses and the distance between objects—this problem tests whether you can track how each factor changes. Use Newton's law of universal gravitation (F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}) to set up a ratio: compare the new force to the old force, and the GG cancels out, leaving you with just the ratio of mass products and distance squares. This ratio approach is much cleaner than calculating actual numbers.

Intuitive explanation

Gravitational force depends on both the masses and the distance between objects—this problem tests whether you can track how each factor changes. Use Newton's law of universal gravitation (F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}) to set up a ratio: compare the new force to the old force, and the GG cancels out, leaving you with just the ratio of mass products and distance squares. This ratio approach is much cleaner than calculating actual numbers.

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