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

Question

The escape velocity from the earth is 11 kms-1. The escape velocity from a planet having twice the radius and same mean density as that of earth is (A) 5.5 kms-1 (B) 11 kms-1 (C) 22 kms-1 (D) None o f the above

Tardigrade Admin · Accepted Answer

Escape velocity, ve=√(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 kms -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 earth is

$5.5 km s^{- 1}$

$11 km s^{- 1}$

$22 km s^{- 1}$

None o f the above

Escape velocity,
$v_{e} = \frac{2 GM}{R} = R \frac{8}{3} π Gρ$
$∴ v_{e} \propto R$ 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 earth is

5.5kms−1

11kms−1

22kms−1