Question

The ratio of radii to the gravitational acceleration of planets X and Y are R and a respectively. The ratio of escape velocities at them, is

• A. $\sqrt{aR}$
• B. $\frac{1}{\sqrt{aR}}$
• C. $aR$
• D. $\frac{1}{aR}$

Answer 1

Answer: (A)

$\sqrt{aR}$

Answer 2

${{v}_{e}}\propto \sqrt{gR}$ Given $\frac{{{R}_{1}}}{{{R}_{2}}}=R$ and $\frac{{{g}_{1}}}{{{g}_{2}}}=a$ $\therefore$ $\frac{{{({{v}_{e}})}_{x}}}{{{({{v}_{e}})}_{y}}}=\sqrt{\frac{{{g}_{1}}{{h}_{1}}}{{{g}_{2}}{{h}_{2}}}}=\sqrt{aR}$