The escape velocity of a body on a planet 'A' is 12 kms -1. The escape velocity of the body on another planet ' B ', whose density is four times and radius is half of the planet ' A ', is :

Question

The escape velocity of a body on a planet 'A' is 12 kms -1. The escape velocity of the body on another planet ' B ', whose density is four times and radius is half of the planet ' A ', is : (A) 12 kms -1 (B) 24 kms -1 (C) 36 kms -1 (D) 6 kms -1

Tardigrade Admin · Accepted Answer

V text escape =√(2 Gm / R ) ⇒ √(2 G ρ × (4/3) π R 3/ R ) V text escape propto √ρ R 2 ∴ if ρ is 4 times and Radius is halved. ⇒ V text escape will remain same

Q. The escape velocity of a body on a planet ' $A$ ' is $12 km s^{- 1}$ . The escape velocity of the body on another planet ' $B$ ', whose density is four times and radius is half of the planet ' $A$ ', is :

$12 km s^{- 1}$

$24 km s^{- 1}$

$36 km s^{- 1}$

$6 km s^{- 1}$

$V_{escape} = \frac{2 G m}{R}$
$\Rightarrow \frac{2 Gρ \times \frac{4}{3} π R ^{3}}{R}$
$V_{escape} \propto ρ R^{2}$
$∴$ if $ρ$ is $4$ times and Radius is halved.
$\Rightarrow V_{escape}$ will remain same

Q. The escape velocity of a body on a planet 'A' is 12kms−1. The escape velocity of the body on another planet ' B ', whose density is four times and radius is half of the planet ' A ', is :

12kms−1

24kms−1

36kms−1

6kms−1