Question

If the earth suddenly contracts so that its radius reduces $4$% with mass remaining same, then what will happen to the escape velocity from earth's surface now?

• A. $\text{Increases by 9}$%
• B. $\text{Decreases by 4}$%
• C. $\text{Increases by 2}$%
• D. $\text{Decreases by 2}$%

Answer 1

The correct option is C $\text{Increases by 2}$%

$V=\sqrt{\frac{2GM}{R}}$

$V\alpha R^{\frac{-1}{2}}$

$\Rightarrow \frac{\Delta V}{V}\times 100=\frac{1}{2}\frac{\Delta R}{R}\times 100$

$\Rightarrow \frac{\Delta V}{V}\times 100=\frac{1}{2}\left[4\right]=2\%$

Increases by 2%

Hence,

option $\left(C\right)$ is correct answer.