Question

What should be the new radius of the earth in order to make the escape velocity to double of the present value without changing the mass of the earth, if the actual radius of the earth is equal to R?

• A. $\frac{2}{R}$
• B. $\frac{4}{R}$
• C. $\frac{R}{4}$
• D. $R^2/2$

Answer 1

The correct option is C $\frac{R}{4}$

We know that $v_e=\sqrt{\frac{2GM}{R}}$

Now if the mass of earth is kept constant, then

$\Rightarrow v_e$ $\alpha$ $\sqrt{\frac{1}{R}}$

This means in order to double the escape velocity, we need to decrese the radius of the earth by 4 times.

Hence correct answer is option $C$