Question

What is the acceleration due to gravity on surface of planet that has radius half of earth and same average density as earth?

Answer 1

Since, Density ρ = Mass/ volume
i.e, Mass, M = ​ρ X V = $\rho \times \frac{4}{3}\pi R^3,whereRistheradiusoftheplanet.$
Given, R = R'/2 , where R' is the radius of the earth= 6.4 X 10⁶ m.
Since, average density of earth = 5.5 X 10³ kg m^-3.
$$\begin{gathered} Since,g=\frac{GM}{R^2} \\ hence,g=\frac{G}{R^2}\times \frac{4}{3}\pi R^3\times \rho =\frac{4}{3}\pi GR\rho ........\left(1\right) \end{gathered}$$
Where, G = 6.67 X 10^-11 N m² kg^-2
Put value of G, R and ​ρ​ in eq. 1 to get your answer.