Question

A sphere of mass 40 kg is attracted by the second sphere of mass 15 kg when their centers are 20 cm apart, with a force of 0.1 milligram weight. Calculate the value of the gravitational constant.

Answer 1

Here,

$m_1=40kg$

$m_2=15kg$

$r=20cm=0.2m$
Weight, $W=0.1mg$ or force, $F=9.8\times {10}^{-6}N$
From the universal law of gravitation, $F=G\frac{m_1{m}_2}{r^2}$ we have,

$G=\frac{F\times r^2}{m1\times m2}$
$\Rightarrow G=\frac{9.8\times {10}^{-6}\times 0.2\times 0.2}{40\times 15}=\frac{0.392\times {10}^{-6}}{600}=6.6\times {10}^{-11}N{m}^2/k{g}^2$