Question

Two masses of 10 kg and 20 kg are separated by a distance of 0.5 m. Calculate the gravitational force between the objects.

Answer 1

Approximately
`5.3* 10^(-8)\; {\rm N}`.

Step-by-step explanation:

Look up the gravitational constant:
`G \approx 6.6743 * 10^(-11)\; {\rm m^(3)\, kg^(-1)\, s^(-2)`.

When two point masses
`M` and
`m` are separated with a distance of
`r`, the gravitational force between the two point masses would be:

`F = (G\, M\, m) / (r^(2))`.

In this question, the masses are
`M = 10\; {\rm kg}` and
`m = 20\; {\rm kg}`. The distance between them is
`r = 0.5\; {\rm m}`. Assuming that the volume of the masses are negligible, the gravitational force between the masses would be:

`\begin{aligned} &(G\, M\, m)/(r^(2)) \\ &= \frac{(6.6743 * 10^(-11)\; {\rm m^(3)\, kg^(-1)\, s^(-2)})\, (10\; {\rm kg})\, (20\; {\rm kg})}{(0.5\; {\rm m})^(2)} \\ &\approx 5.3\; {\rm kg \cdot m\cdot s^(-2) \\ &= 5.3\; {\rm N}\end{aligned}`.