Question

The gravitational attraction between a 20 kg cannonball and a marble separated center-to-center by 30 cm is 1.48 x 10 ^ -10 N. Compute the mass of the marble.

Answer 1

The gravitational attraction between two masses $m_1,m_2$ is given as follows:

$$F = G\dfrac{m_1m_2}{r^2}$$

where $m_1 = 20kg$, $m_2$ is the mass of the marble, $r = 30cm = 0.3m$ is the distance between centers, and $G = 6.67\times 10^{-11}m^3/(kg\cdot s^2)$ . Expressing $m_2$ and substituting $F = 1.48\times 10^{-10}N$, obtain:

$$m_2 = \dfrac{r^2F}{m_1G}\\ m_2 = \dfrac{0.3^2\cdot 1.48\times 10^{-10}}{30\cdot 6.67\times 10^{-11}} \approx 6.66\times 10^{-3}kg$$

Answer. $6.66\times 10^{-3}kg$.