Question

For a planet having mass equal to mass of the earth but radius is one fourth of radius of the earth. Then escape velocity for this planet will be

Answer 1

Escape velocity =√2Rg

Radius of planet=1/4 Radius of earth

Radius of earth=4 Radius of planet

Escape velocity of planet =√2(4R)g

=2√2Rg

=2*11.2

=22.4

Answer 2

The escape velocity for this planet will be 22.4 km/s.

Explanation:

Let m is the mass of the Earth as well as that of planet. If r is the radius of the Earth such that,

r' = (1/4) r, r' is the radius of the planet

The escape velocity of earth is equal to 11.2 km/s and the relation to find it is given by :

The escape velocity of this planet is,

$v'=\sqrt{\dfrac{Gm}{r'}}$

$v'=\sqrt{\dfrac{Gm}{(r/4)}}$

$v'=2\times \sqrt{\dfrac{Gm}{(r)}}$

$v'=2\times 11.2$

v' = 22.4 km/s

So, the escape velocity for this planet will be 22.4 km/s. Hence, this is the required solution.

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