Question

If mass of 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

Question

In the ABO system of blood groups if both antigens are present but no antibody, the blood group of the individual would be :-

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.