Question

The escape velocity from earth is $11.2\,km \,s ^{-1}$. Another planet is having mass $1000$ times and radius $10$ times that of the earth, then escape velocity at that planet will be:

• A. 11.2 km/s
• B. 112 km/s
• C. 1.12 km/s
• D. 1120 km/s

Answer 1

Answer: (B)

The escape velocity at earth is given by
$v_{e}=\sqrt{\frac{2 G M_{e}}{R_{e}}}$
where G is gravitational constant,
$ M_e$ and $R_e $ are mass and radius of earth respectively
$=v_{p}=\sqrt{\frac{2 G M_{p}}{R_{p}}}$ (planet) .....(i)
Given $M_{p}=1000 M_{e}, $
$R_{p}=10 R_{e}$
$=\frac{v_{p}}{v_{e}}=\sqrt{\frac{2 G \times 1000 M_{e}}{10 R_{e}} \times \frac{R_{e}}{2 G M_{e}}}$
$=v_{p}=10 v_{e}$
$=v_{p}=10 \times 11.2$
$=v_{p}=112 \,kms ^{-1}$