Question

The gravitational force between two objects that are 0.11 m apart is 3.5x10^-6 N. If the mass of one object is 58 kg what is the mass of the other object?

Answer 1

Approximately
`11\; {\rm kg}`.

Step-by-step explanation:

Look up the Gravitational Constant
`G`:

`G \approx 6.6743 * 10^(-11)\; {\rm N\cdot m^(2) \cdot kg^(-2)}`.

When two objects of mass
`M` and
`m` respectively are at a distance of
`r` away from one another, the gravitational attraction between them would be:

`\begin{aligned}F &= (G\, M\, m)/(r^(2))\end{aligned}`.

In this question, it is given that
`F = 3.5 * 10^(-6)\; {\rm N}`,
`M = 58\; {\rm kg}`, and
`r = 0.11\; {\rm m}`. Rearrange the equation to find
`m`, the mass of the other object:

`\begin{aligned}m &= (r^(2)\, F)/(G\, M) \\ &\approx ((0.11)^(2)\, (3.5 * 10^(-6)))/((6.6743* 10^(-11))\, (58))\; {\rm kg} \\ &\approx 11\; {\rm kg}\end{aligned}`.