Question

If 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

Explanation:

Twice that of Earth........

Bblegend

Answer 2

Given :

Mass of a planet is eight times the mass of earth

Radius of a planet is twice the radius of earth

To Find :

Escape velocity for that planet

Solution :

Escape velocity for a planet is given by ,

$\\ \star \: {\boxed{\purple{\sf{v = \sqrt{ \dfrac{2GM }{R} } }}}}$

Where ,

M is mass of planet

R is radius of planet

Let the mass of earth be M and radius be R. Then the mass of a planet becomes 8M and radius becomes 2R [given condition].

Now , Calculating escape velocity for earth ;

$\\ : \implies \sf \:v_{(earth)} = \sqrt{ \dfrac{2GM }{ R} } \: .........(1)$

Now , Calculating escape velocity of the planet ;

$\\ : \implies \sf \: v_{(planet)} = \sqrt{\dfrac{2(8M)}{(2 R)} }$

$\\ : \implies \sf \: v_{(planet)} = \sqrt{ \dfrac{2(4M )}{R} }$

$\\ : \implies \sf \: v_{(planet)} = 2 \sqrt{ \dfrac{2GM }{R} }$

$\\ : \implies \sf \: v_{(planet)} = 2[ v_{(earth)} ]$

Escape velocity of earth is 11.2 km/s. Now,

$\\ : \implies \sf \: v_{(planet)} = 2 \times 11.2 \: km. {s}^{ - 1}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{v_{(planet)} = 22.4 \: km .{s}^{ - 1} }}}}} \: \bigstar$

Hence ,

The escape velocity of a planet whose mass of planet is eight eight time mass of earth and radius is twice of the radius of the earth is 22.4 km/s.