Question

Estimate the acceleration due to gravity at the surface of Europa (one of the moons of Jupiter) given that its mass is 4.9×1022kg and making the assumption that its mass per unit volume is the same as Earth's.

Answer 1

Answer:$g=1.97 m/s^2$

Explanation:

Given

mass of Jupiter is $M=4.9\times 10^{22} kg$

Density of Jupiter is same as Earth

$density\ of\ Earth=density\ of\ Jupiter=5510 kg/m^3$

$mass=volume\times density$

considering Jupiter to be sphere of radius r

$M=\frac{4}{3}\times \pi r^3\times \rho$

$r^3=\frac{3M}{\rho \times 4\pi}$

$r^3=\frac{3\times 4.9\times 10^{22}}{5510\times 4\pi}$

$r=(\frac{3\times 4.9\times 10^{22}}{5510\times 4\pi})^{\frac{1}{3}}$

$r=1.28\times 10^6 m$

acceleration due to gravity is given by

$g=\frac{GM}{r^2}$

$g=\frac{6.67\times 10^{-11}\times 4.9\times 10^{22}}{(1.28\times 10^6)^2}$

$g=1.97 m/s^2$