Question

The radius in kilometres to which the present radius of the earth $(R=6400km)$ is to be compressed so that the escape velocity is increased to $10$ times is:

• A. $6.4$
• B. $64$
• C. $640$
• D. $4800$

Answer 1

The correct option is B $64$

The escape velocity $v_e=\sqrt{2gR}$

Here, $v_e=10v_e^{\prime }$

or $\sqrt{2gR}=10\sqrt{2g{R}^{\prime }}$

or $R^{\prime }=R/100=6400/100=64$ km