Two small spheres

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Two small spheres, initially of masses m1=200 kgm_1 = 200\,\text{kg} and m2=500 kgm_2 = 500\,\text{kg}, are placed with their centres 2.0 m2.0\,\text{m} apart in empty space. (i) Calculate the magnitude of the gravitational force F1F_1 between the spheres. Take G=6.67×10−11 N m2/kg2G = 6.67\times10^{-11}\,\text{N m}^2\text{/kg}^2. (ii) Both masses are now doubled while, simultaneously, the centre-to-centre separation is increased to three times its initial value. Determine the new gravitational force F2F_2. (iii) Show that the ratio F2/F1F_2/F_1 is 49\dfrac{4}{9} and verify that your numerical answers are consistent with this ratio.

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