Question

What should be the new radius of the earth, in order to reduce the escape velocity to half of the present value without changing the mass of the earth?

• A. $\frac{R}{2}$
• B. $2R$
• C. $3R$
• D. $4R$

Answer 1

The correct option is D $4R$

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

$\Rightarrow R$ $\alpha$ $\frac{1}{v_e^2}$

Now if $v_e$ is reduced to half then $R$ will become $4R$

Hence correct answer is option $D$