If the escape velocity of a planet is 3 times that of the earth and its radius is 4 times that of the earth, then the mass of the planet is
(Mass of the earth `= 6 xx 10^(24) kg`)

Options

A. `1.62 xx 10^(22) kg`
B. `0.72 xx 10^(22) kg`
C. `2.16 xx 10^(26) kg`
D. `1.22 xx 10^(22) kg`

Answer

C

Explanation

Escape velocity of a planet
`= 3 xx` Escape velocity of the earth
`sqrt((2GM_(P))/(R_(P))) = 3 sqrt((2 GM_(e))/(R_(e)))`
`(M_(p))/(R_(p)) = 9(M_(e))/(R_(e))`
`(M_(p))/(4R_(e)) = 9(M_(e))/(R_(e))`
`therefore M_(p) = 36 M_(e) = 36 xx 6 xx 10^(24)`
`= 2.16 xx 10^(26)kg`