Question

If acceleration due to gravity on the surface of a planet is two times that on the surface of the earth and its radius is double that of earth then, escape velocity from the surface of that planet in comparison to earth will be

• A. $2v_e$
• B. $3v_e$
• C. $4v_e$
• D. None of these

Answer 1

The correct option is A

$2v_e$

Solution:

Step 1: Given data

A planet's radius is twice as large as the earth's, and its surface acceleration caused by gravity is two times that of Earth.

Step 2: Formula used

Know that the escape velocity is $v_e=\sqrt{2gR}$, here $g$ gravity and$R$ is the radius.

Step 3: Calculate the velocity

Note that if the radius and gravity are doubled,

Then new escape velocity will be,

$$\begin{gathered} v\text{'}=\sqrt{2\times 2g\times 2R} \\ v\text{'}=2\sqrt{2gR} \\ v\text{'}=2v_e \end{gathered}$$

Consequently, the planet's surface will have a greater escape velocity than Earth

Hence, the correct option is A.