Question 56: Gravitation

Question

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

Accepted Answer

The escape velocity ($v_{	ext{esc}}$) for a planet with mass $M$ and radius $R$ is given by the formula:
$$ v_{	ext{esc}} = \sqrt{\frac{2GM}{R}} $$
where $G$ is the gravitational constant.
For Earth, let's denote its mass as $M_E$ and its radius as $R_E$. The escape velocity is given as 11.2 km/s. Therefore:
$$ v_{	ext{esc, Earth}} = \sqrt{\frac{2G M_E}{R_E}} = 11.2 	ext{ km/s} $$
For the planet in question, its mass $M_P$ is $M_E/8$ and its radius $R_P$ is $R_E/2$. The escape velocity from the planet is:
$$ v_{	ext{esc, Planet}} = \sqrt{\frac{2G M_P}{R_P}} = \sqrt{\frac{2G (M_E/8)}{R_E/2}} $$
Simplifying the expression:
$$ v_{	ext{esc, Planet}} = \sqrt{\frac{2G (M_E/8)}{R_E/2}} = \sqrt{\frac{2G M_E \cdot 2}{8R_E}} = \sqrt{\frac{G M_E}{2R_E}} $$
Now, relate it to the escape velocity from Earth:
$$ v_{	ext{esc, Planet}} = \frac{1}{\sqrt{4}} \cdot v_{	ext{esc, Earth}} $$
Calculating further:
$$ v_{	ext{esc, Planet}} = \frac{1}{2} \cdot 11.2 	ext{ km/s} = 5.6 	ext{ km/s} $$
Thus, the escape velocity from the planet is 5.6 km/s.
Option C: 5.6 km/s
is the correct answer.

Answer

8.4

Answer

11.2

Answer

5.6

Answer

2.8

Gravitation

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

Choose the correct answer: