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)

5m/s2

Answer 2

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 𝑔 g at the surface of the planet is given by:
$g=\frac{GM}{R^2}$
We already found 𝐺𝑀 GM , 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