Question

Escape velocity from the Earth is 11.2 km/s Another planet of same mass has radius 1/4 times that of the earth what is the escape velocity from another planet?​

Answer 1

Explanation:

Escape velocity, ve = 2GM

Re

11.2km/s

For R' =

Re

4

M' = Me

2GM Re 4 = 2ve = 22.4km/s

Answer 2

Explanation:

Problem Solving Strategy!

Compare the equation of escape velocity of Earth and planet. Escape velocity is given by,

ves. = √ ( 2GMe / Re )

From a planet, ves. = √2GMp / Rp

Therefore ves / ves = [ √2 GMp / Rp ] × [ Re / 2GMe ]

It given that,

Mass of the planet = mass of the earth

i.e = Mp = Me

So, v'es / ves = √ Re / Rp _[i]

Given,

Rp = Re / 4 => Rp / Re = 1/4 and ves = 112 km/s

Substituting in Eq [i] we have

v'es / 11.2 = √4/1 = 2,

v'es = 11.2 × 2 = 22.4 km/s

∴ Escape Velocity ( v'es) of another planet is 22.4 km/s!