Chapter 13: Q. 8 (page 353)

The escape speed from Planet X is 10,000 m/s. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?

Short Answer

Expert verified

Escape velocity of Planet Y is 14140 m/sec

Step by step solution

Given Information

Escape velocity of planet X, is 10000 m/s
Density of planet Y is twice the density of planet X => ρ_x = 2ρ_y

Radius of planet Y is equal to the radius of planet X => R_x = R_y

Explanation

We can calculate escape velocity as

$v_{e} = \sqrt{\frac{2 G M}{r}}$

Where G = universal gravitational constant, M = mass of the planet
r = radius of the planet

The escape velocity of planet X is

$v_{X} = \sqrt{\frac{2 G M}{R_{X}}} = \sqrt{\frac{2 G ρ_{X} V}{R_{X}}} (as M = ρ \times V)$

And for plant Y is

$v_{Y} = \sqrt{\frac{2 G M}{R_{Y}}} = \sqrt{\frac{2 G ρ_{Y} V}{R_{Y}}} (as M = ρ \times V)$

Now get the ratio and substitute values given

$\frac{v_{X}}{v_{Y}} = \frac{\sqrt{\frac{2 G ρ_{X} V}{R_{X}}}}{\sqrt{\frac{2 G ρ_{Y} V}{R_{Y}}}} \frac{10000 m / s}{v_{Y}} = \sqrt{\frac{ρ_{X}}{2 ρ_{X}}} v_{Y} = 14140 m / s$

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The escape speed from Planet X is 10,000 m/s. Planet Y has the same radius as Planet X but is twice as dense. What is the escape speed from Planet Y?

Short Answer

Step by step solution

Given Information

Explanation

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