Question

If the Earth were made of wood, the mass of wooden earth is $10$% as much as it is now without the change in its diameter.
Calculate the escape velocity of space shot from the surface of wooden earth.
Radius of earth: $R=6400km$
Mass of earth: $M=6\times {10}^{24}kg$
Constant of gravitation: $G=6.67\times {10}^{-11}N{m}^2/k{g}^2$

Answer 1

If the earth were wooden, its mass $\left(M_w\right)$ would be $\frac{M}{10}$. Hence its escape speed $\left(V_{ew}\right)$ is given by
$V_{ew}=\sqrt{\frac{2G{M}_w}{R}}$
$=\sqrt{\frac{2GM}{10R}}$
$=\sqrt{\frac{2\times 6.67\times {10}^{-11}\times 6\times {10}^{24}}{10\times 6400\times {10}^3}}$
$=3.54\times {10}^{3}m/s$