Question

A planet has an escape speed of 10km/s,The radius of the planet is 10,000km. The acceleration due to gravity of the planet at its surface is:

• A. 10m/s²
• B. 9.8m/s²
• C. 20m/s²
• D. 2.5m/s²
• E. 5m/s²

Answer 1

Answer: (E)

The correct answer is (E): 5m/s²
\(v_e=\sqrt\frac{2GM}{R}\)
First, solve for \(\frac{GM}{R}\)
\(v^2_e=\frac{2GM}{R}\)
\(GM =5 \times10^{14}m^3/s^2\)
Next, the acceleration due to gravity 𝑔g at the surface of the planet is given by:
\(g=\frac{GM}{R^2}\)
We already found 𝐺𝑀GM, so we can substitute:
\(g=\frac{5\times10^{14}m^3/s^2}{(10,000,000 \, m)^2}\)
g= 5m/s²
Thus, the acceleration due to gravity at the surface of the planet is 5m/s25m/s²