Question

Calculate the energy needed for moving a mass of $4kg$ from the centre of the earth to its surface (in multiple of ${10}^8$ joule), if radius of the earth is 6400 $km$ and acceleration due to gravity at the surface of the earth is $g=10m/s^2$

Answer 1

Given:
Mass(m)=$4kg$
Radius of Earth$\left(R\right)=6400km$
Acceleration due to gravity$\left(g\right)=10m/s^2$
$U_i=\frac{-3GMm}{2R}\dots \left(i\right)$
$U_f=\frac{-GMm}{R}\dots \left(ii\right)$
$\Delta U=U_f-U_i$
$\Delta U=\frac{GMm}{2R}=-\frac{mgR}{2}$
Hence, by putting the values we get,
$\Delta U=\frac{4\times 10\times 6.4\times {10}^6}{2}$
$\Delta U=1.28\times {10}^{8}J$
Final Answer: 1.28