Question

If the mass of a planet is eight times the mass of the earth and its radius is
twice the radius of the earth, what will be the escape velocity for that planet?​

Answer 1

Mass of planet M = 8 x mass of earth = 8 x 6 x 1024 kg

Radius of planet R = 2 x radius of earth = 2 x 6.4 x 106 m

G = gravitational constant = 6.67 x 10-11 N m2/kg2

So escape velocity = √

Escape velocity =

= 22.4 km/sec.

So escape velocity of the planet will be 22.4 km/sec.

Answer 2

Answer:

Given:

Mass of planet = 8 times mass of Earth

Radius= 2 times of Radius of Earth

To find:

Escape Velocity for that planet.

Formulas:

Let mass of Earth be m, radius of Earth be r and universal gravitational constant be G.

Let escape Velocity from Earth be v.

$escape \: vel. = \sqrt{ \frac{2Gm}{r} }$

Calculation:

Let escape Velocity for the planet be v2,

mass be 8m , radius be 2r.

$escape \: vel. of \: planet= \sqrt{ \frac{2G(8m)}{2r} }$

$= > v2= \sqrt{ 4( \frac{2Gm}{r} )}$

$= > v2= 2 \sqrt{ ( \frac{2Gm}{r} )}$

$= > v2= 2(escape \: vel. \: from \: earth)$

$= > v2= 2(v)$

So final answer:

Escape Velocity from the planet will be twice as compared to that of Earth.

As per data, we know that Escape Velocity from Earth surface = 11.2 km/s.

So in the given planet, escape Velocity will be :

v" = 2 × 11.2 = 22.4 km/s.