Question

You are exploring a small moon of a distant planet. Measurements indicate that this moon is a sphere of uniform density rho = 5000 kg/m3. You dig a very deep hole into the moon that reaches within r0 = 1000 m of the center of the moon. With your spacesuit, you have a mass of m = 85 kg. Find the force of gravity on you when you stand at the bottom of the hole.

Answer 1

The force of gravity will be "0.11874 N"

Step-by-step explanation:

The given values are:

Density of planet,

Q = 5000 Kg/m³

Inside radius,

r₀ = 1000 m

Now,

The mass of inside sphere will be:

⇒
`m_p=density* volume`

⇒
`=5000* (4)/(3)\pi r^3`

On putting the values, we get

⇒
`=5000* (4)/(3)* \pi* (1000)^3`

⇒
`=85 \ kg`

hence,

The force of gravity will be:

=
`(Gm_(planet) m_(person))/(r^2)`

=
`(6.67* 10^(-11)* 5000* 4\pi* 85* 1000)/(3)`

=
`(6.67* 10^(-11)* 4\pi* 425000000)/(3)`

=
`0.11874 \ N`