Question

What is the average density of Neptune if the acceleration due to gravity on its surface is 11 m/s2 and its radius is 2.48 107 m

Answer 1

Density of Neptune is 1581 kg/m³  

Explanation:

Acceleration due to gravity is given by

            $g=\frac{GM}{R^2}$

     G =6.67 x 10⁻¹¹ Nm²/kg²

      M = Mass

      R = Radius

Substituting

            $11=\frac{6.67\times 10^{-11}\times M}{(2.48\times 10^7)^2}\\\\M=1.01\times 10^{26}kg$

Mass of Neptune is 1.01 x 10²⁶ kg

Now we have equation for volume,

               $V=\frac{4}{3}\pi R^3\\\\V=\frac{4}{3}\pi (2.48\times 10^7)^3=6.39\times 10^{22}m^3$

We have

          Mass = Volume x Density

           1.01 x 10²⁶ = 6.39 x 10²² x Density

           Density = 1581 kg/m³  

Density of Neptune is 1581 kg/m³