Question

Suppose a planet exists whose mass and radius both are half those of the earth. Calculate the acceleration due to gravity on the surface of this planet

Answer 1

Mass and radius both are half of those of the earth
g (acceleration due to gravity) = ?
G (gravitational constant) = 6.673 × 10⁻¹¹ Nm² kg⁻²
M (mass of new planet)= (5.98 × 10²⁴ kg)/2
R (radius of the earth) = (6.4 × 10⁶ m)/2
$$\begin{gathered} \mathbf{g}\mathbf{=}\frac{\mathbf{GM}}{{\mathbf{R}}^{\mathbf{2}}} \\ \mathbf{}=\frac{6.673\times {10}^{-11}\times 5.98\times {10}^{24}\times 4}{{\left(6.4\times {10}^6\right)}^2\times 2} \\ \mathbf{}=\frac{6.673\times {10}^{-11}\times 5.98\times {10}^{24}\times 4}{6.4\times 6.4\times {10}^{12}\times 2}\left({{10}^{24}}^{-11}={10}^{13}\right) \\ \mathbf{}=\frac{6.673\times 5.98\times 4\times {10}^{14}}{6.4\times 6.4\times {10}^{12}\times 2}\left({{10}^{13}}^{-12}=10\right) \\ \mathbf{}=\frac{6.673\times 5.98\times 4\times 10}{6.4\times 6.4\times 2} \\ \mathbf{}=\frac{159.61816\times 10}{6.4\times 6.4\times 2} \\ \mathbf{}=1.9484\times 10\mathbf{}=19.5\mathrm{N} \end{gathered}$$