Physics

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: a. (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. b. (ii) Calculate the numerical value of

g_{X}

. c. (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.

Intuitive explanation

Surface gravity depends on both the planet's mass and how far you are from its center. Since Planet X is more massive but also larger, these effects work against each other—you need to set up the ratio $g_X/g_E$ using the gravitational acceleration formula $g = GM/R^2$ to see which effect wins out.

Intuitive explanation

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