Question

The eacape velocity from earth is 11km/s. The escape velocity from a planet having twice the radius and same mean density as that of earth is

Answer 1

Escape Velocity ve=2GMeRe‾‾‾‾‾‾‾√
v
e
=
2
G
M
e
R
e
=2G(43πρR3ed)Re‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾⎷
=
2
G
(
4
3
π
ρ
R
e
3
d
)
R
e
=2G(43πρR2e)d‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
=
2
G
(
4
3
π
ρ
R
e
2
)
d
=> veαR
v
e
α
R
Since density is same.
When radius is doubled escape velocity gets doubled
2ve=2×11=22km/s