The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is

Question

The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is (A)  √3 v  (B)  √2 v  (C)  √5 v  (D)  √12 v

Tardigrade Admin · Accepted Answer

Escape velocity from the earth ve=√(2GM/R) For a given planet vp=√(2G(6M)/2R)=√3ve=√3v

Q. The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is $v,$ then the escape velocity from the planet is

$3 v$

$2 v$

$5 v$

$12 v$

Escape velocity from the earth
$v_{e} = \frac{2 GM}{R}$
For a given planet
$v_{p} = \frac{2 G ( 6 M )}{2 R} = 3 v_{e} = 3 v$

Q. The mass of a planet is six times that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is v, then the escape velocity from the planet is

3​v

2​v

5​v

12​v