A uniformly massive spherical shell has radius $3\times 10^6,\text{m}$ and total mass $4\times 10^{20},\text{kg}$. What is the magnitude of the gravitational field at a point $6\times 10^6,\text{m}$ from the centre?

Step-by-step solution

1. Use Gauss’s law for gravitation: $E=GdfracM{r}^2$ for points outside a spherical shell.
2. Take $G=6.674\times 10^{-11},{\text{N,m}}^2{\text{/kg}}^2$, $M=4\times 10^{20},\text{kg}$, $r=6\times 10^6,\text{m}$.
3. Compute numerator: $G,M=6.674\times 10^{-11}\times 4\times 10^{20}=2.6696\times 10^{10},{\text{N,m}}^2\text{/kg}$.
4. Compute denominator: $r^2=(6\times 10^6{)}^2=3.6\times 10^{13},{\text{m}}^2$.
5. Divide: $E=2.6696\times 10^{10}/3.6\times 10^{13}=7.4111\times 10^{-4},\text{N/kg}$.
6. Express as $7.41\times 10^{-4},\text{N/kg}$.

Concept tested: Gauss’s law for gravity

Published 4 October 2026 · How this solution was prepared and checked