A planet having mass 9 M e and radius 4 R e , where M e and R e are mass and radius of earth respectively, has escape velocity in km s - 1 given by: (Given escape velocity on earth V e = 11 . 2 × 10 3

Question

A planet having mass 9 M e and radius 4 R e , where M e and R e are mass and radius of earth respectively, has escape velocity in km s - 1 given by: (Given escape velocity on earth V e = 11 . 2 × 10 3 m s - 1 )

TestHub · Accepted Answer

The escape velocity on earth is given by $V_{e} = \sqrt{\frac{2 G M_{e}}{R_{e}}}$
Escape velocity for the planet is
$V'_{e s c} = \sqrt{\frac{2 G (9 M_{e})}{4 R_{e}}} . . . (i)$
The escape velocity of earth is $V_{e} = 11.2 \times 10^{3} m s^{- 1}$
From equation (i)
$V'_{e s c} = \sqrt{\frac{9}{4} (\frac{2 G M_{e}}{R_{e}})} = \frac{3}{2} \times 11.2 \times 10^{3} m s^{- 1} \Rightarrow V'_{esc} = 16.8 km s^{- 1}$

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