Planet X has mass twice that of the Earth and radius times the Earth’s radius

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Planet X has mass twice that of the Earth and radius

1.5

times the Earth’s radius. Taking the acceleration due to gravity on the surface of Earth as

g_{E}=9.8\,\text{m}\,\text{s}^{-2}

and the mass and radius of Earth as

M_{E}

and

R_{E}

respectively, answer the following: (i) Derive an expression for the acceleration due to gravity

g_{X}

on the surface of Planet X in terms of

g_{E}

, the mass ratio and the radius ratio. (ii) Calculate the numerical value of

g_{X}

. (iii) Find the weight of a

2.0\,\text{kg}

object on the surface of Planet X and compare it with its weight on Earth.