Question

Within a certain type of star called a neutron star, the material at the center has a mass density of 1.0 × 1018 kg/m3. if a tiny sphere of this material of radius 1.0 × 10–5 m were somehow transported to the surface of the earth, what would be the weight of this sphere?

Answer 1

First we need to calculate the mass of the tiny sphere, which is given by

`m=dV`
where
d is the density
V is the volume

Given the radius of the sphere, r, its volume is

`V= (4)/(3) \pi r^3= (4)/(3) \pi (1.0 \cdot 10^(-5)m)^3 =4.2 \cdot 10^(-15) m^3`

So now we can calculate the mass of the sphere

`m=dV=(1.0 \cdot 10^(18) kg/m^3)(4.2 \cdot 10^(-15) m^3)=4187 kg`

And the weight of the sphere at the Earth surface, where the gravitational acceleration is
`g=9.81 m/s^2`, would be

`W=mg=(4187 kg)(9.81 m/s^2)=41074 kg`