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:

Option 1 - 12 kms-1

Option 2 - 24 kms-1

Option 3 - 36 kms-1

Option 4 - 6 km-1

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Alok Kumar Singh | Contributor-Level 10

6 months ago

Correct Option - 1

Detailed Solution:

$M_{A} = ρ_{A} * \frac{4}{3} π R_{A}^{3}$ $ρ_{B} = 4 ρ_{A}$

$M_{B} = ρ_{B} * \frac{4}{3} π R_{B}^{3}$ $R_{B} = \frac{R_{A}}{2}$

$\frac{M_{A}}{M_{B}} = 2, \frac{R_{A}}{R_{B}} = 2$ $\frac{V_{E A}}{V_{E B}} = \sqrt[]{\frac{2 G_{1} M_{A}}{R_{A}} * \frac{R_{B}}{2 G_{1} M_{B}}}$

$v_{E A} = v_{E B} = 12 k m s e c^{- 1}$

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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:

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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: