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Question: The escape velocity of a planet having mass 6 times and radius 2 times as that of earth is...

The escape velocity of a planet having mass 6 times and radius 2 times as that of earth is

A

3Ve\sqrt { 3 } V _ { e }

B

3Ve3 V _ { e }

C

2Ve\sqrt { 2 } V _ { e }

D

2Ve2 V _ { e }

Answer

3Ve\sqrt { 3 } V _ { e }

Explanation

Solution

vpve=MpMe×ReRp=6×12=3\frac { v _ { p } } { v _ { e } } = \sqrt { \frac { M _ { p } } { M _ { e } } \times \frac { R _ { e } } { R _ { p } } } = \sqrt { 6 \times \frac { 1 } { 2 } } = \sqrt { 3 } ∴vp=3ve\therefore v _ { p } = \sqrt { 3 } v _ { e }