Question

If the radius of earth and acceleration due to gravity on surface both are doubled, escape velocity of a satellite from surface of earth will become

• A. $11.2\text{km/s}$
• B. $22.4\text{km/s}$
• C. $5.6\text{km/s}$
• D. $44.8\text{km/s}$

Answer 1

The correct option is B $22.4\text{km/s}$

Escape velocity $v=\sqrt{\frac{2GM}{R}}$
or $v=\sqrt{2gR}.$

If $g$ and $R$ are doubled, then
$v=\sqrt{2\left(2g\right)\left(2R\right)}=2\sqrt{2gR}$
$i.e.,v=2\times 11.2=22.4\text{km/s}$