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

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

Tardigrade Admin · Accepted Answer

Escape velocity, v textescape=√(2 G M/R) =R√(8/3) π G ρ ∴ ve propto R if ρ = constant. Since the planet is having double radius in comparision to earth, therefore escape velocity becomes twice i.e, 22 k m s- 1 .

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

$5.5 km s^{- 1}$

$11 km s^{- 1}$

$22 km s^{- 1}$

None of these

Escape velocity,
$v_{escape} = \frac{2 GM}{R}$
$= R \frac{8}{3} π Gρ$
$∴ v_{e} \propto R$ if $ρ =$ constant.
Since the planet is having double radius in comparision to earth, therefore escape velocity becomes twice i.e, $22 km s^{- 1}$ .

Q. The escape velocity from the earth is 11kms−1 . The escape velocity from a planet having twice the radius and same mean density as that of the earth is

5.5kms−1

11kms−1

22kms−1