Question

The escape velocity from the earth is $11 \, k m \, s^{- 1}$ . The escape velocity from a planet having twice the radius and same mean density as that of the earth is

• A. $5.5 \, k m \, s^{- 1}$
• B. $11 \, k m \, s^{- 1}$
• C. $22 \, k m \, s^{- 1}$
• D. None of these

Answer 1

Answer: (C)

Escape velocity,
$ \, \, \, v_{\text{escape}}=\sqrt{\frac{2 \, G M}{R}} \, \, $
$ \, \, =R\sqrt{\frac{8}{3} \pi G \rho }$
$\therefore v_{e} \propto R \,$ if $ \, \rho =$ constant.
Since the planet is having double radius in comparision to earth, therefore escape velocity becomes twice i.e, $22 \, k m \, s^{- 1}$ .