Question

The gravitational constant G was first measured accurately by Henry Cavendish in 1798. He used an exquisitely sensitive balance to measure the force between two lead spheres whose centers were 0.27 m apart. One of the spheres had a mass of 188 kg, while the mass of the other sphere was 0.93 kg.
What was the ratio of the gravitational force between these spheres to the weight of the lighter sphere?

Answer 1

The gravitational force between the spheres is

$F_{\rm g}=\dfrac{G(188\,\mathrm{kg})(0.93\,\mathrm{kg})}{(0.27\,\mathrm m)^2}\approx1.6\times10^{-7}\,\mathrm N$

where G = 6.674 x 10⁻¹¹ N m²/kg².

The weight of the lighter sphere is

$F_{\rm w}=(0.93\,\mathrm{kg})g\approx9.1\,\mathrm N$

where g = 9.80 m/s².

The ratio between the two forces is then

$\dfrac{F_{\rm g}}{F_{\rm w}}\approx1.8\times10^{-8}$