Question

Two objects, one with a mass of 75.0kg and the other with a mass of 60.0kg experience a gravitational force of attraction of 8.50x10-9N. How far apart are their

centers of mass?

Answer 1

Approximately
`5.94\; {\rm N}`.

Step-by-step explanation:

The gravitational force between two objects of uniform mass is:

`\displaystyle F = (k\, M\, m)/(r^(2))`,

Where:

• 
  `k \approx 6.67 * 10^(-11)\; {\rm m^(3)\, kg^(-1)\, s^(-2) }` is the gravitational constant,
• 
  `M` and
  `m` are the mass of the two objects, and
• 
  `r` is the distance between the center of mass of the two objects.

Rearrange this equation to find
`r`:

`\begin{aligned} r &= \sqrt{(k\, M\, m)/(F)} \\ &= \sqrt{((6.67 * 10^(-11))\, (75.0)\, (60.0))/(8.50 * 10^(-9))}\; {\rm kg} \\ &\approx 5.94\; {\rm kg}\end{aligned}`.