Question

The mass of the moon is $1/81$ of earth's mass and it's radius $1/4$ that of the earth. If the escape velocity from the earth's surface is $11.2$ km/sec, it's value for the moon will be.

• A. $0.14$ kms^-1
• B. $0.5$ kms^-1
• C. $2.5$ kms^-1
• D. $5.0$kms^-1

Answer 1

The correct option is C

$2.5$ kms^-1

Step 1: Escape velocity

For earth,

Escape velocity $V_e=\sqrt{\frac{2GM}{R}}$

Where,

$G$ is universal gravitational constant

$M$ is mass

$R$is radius.

Step 2; Finding escape velocity in the moon

For moon,

$$\begin{gathered} V{\text{'}}_e=\sqrt{\frac{2GM\text{'}}{R\text{'}}} \\ \frac{V{\text{'}}_e}{V_e}=\sqrt{\frac{RM\text{'}}{MR\text{'}}} \\ =\sqrt{\frac{RM\times 4}{81\times RM}} \\ V{\text{'}}_e=v_e\sqrt{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$81$}\right.} \\ {V}_e=11.2\times \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$9$}\right. \\ {V}_e=2.489\simeq 2.5Km/sec \end{gathered}$$

Hence, the correct answer is option (c) 2.5 Km/sec.