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

Question

The escape velocity of a body on a planet A is 12 &#160; km &#160; 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

Aicharya · Accepted Answer

We know that escape velocity is given by,

$v = \sqrt{\frac{2 G M}{R}} \Rightarrow \frac{v_{A}}{v_{B}} = \sqrt{\frac{M_{A}}{M_{B}} \times \frac{R_{B}}{R_{A}}} = \sqrt{\frac{ρ_{A} {R_{A}}^{3}}{ρ_{B} {R_{B}}^{3}} \times \frac{R_{B}}{R_{A}}} = \sqrt{\frac{ρ_{A} {R_{A}}^{2}}{ρ_{B} {R_{B}}^{2}}} = \sqrt{\frac{1}{4} \times \frac{4}{1}} \Rightarrow v_{B} = v_{A} = 12 km s^{- 1}$

The escape velocity of a body on a planet A is 12   km   s - 1 . The escape velocity of the body…

Solution

The escape velocity of a body on a planet A is 12 &#160; km &#160; s - 1 . The escape velocity of the body…

Solution

The escape velocity of a body on a planet A is 12 km s - 1 . The escape velocity of the body…