Question

A 3.0kg cat and a 14kg dog exert a force of gravity on each other equal to 1.12 x 10^-10 N. how far apart are they

Answer 1

The expression for the gravitational force between two bodies is given by:

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

where,

G: Cavendish's constant = 6.67*10-11Nm^2/kg^2

m1 = 3.0kg

m2 = 14kg

Solve the equation above for r:

$\begin{gathered} r=\sqrt{\frac{Gm_1m_2}{F}} \\ r=\sqrt[]{\frac{(6.67\cdot10^{-11}\frac{Nm^2}{\operatorname{kg}^2})(3.0kg)(14kg)}{10\cdot10^{-10}N}} \\ r\approx1.67m \end{gathered}$

Hence, the distance between the dog and the car is approximately 1.67m