The escape velocity from earth is 11.2 km s -1. Another planet is having mass 1000 times and radius 10 times that of the earth, then escape velocity at that planet will be:

Question

The escape velocity from earth is 11.2 km s -1. Another planet is having mass 1000 times and radius 10 times that of the earth, then escape velocity at that planet will be: (A) 11.2 km/s (B) 112 km/s (C) 1.12 km/s (D) 1120 km/s

Tardigrade Admin · Accepted Answer

The escape velocity at earth is given by

v_{e} = \frac{2 G M _{e}}{R _{e}}

where G is gravitational constant,

M_{e}

and

R_{e}

are mass and radius of earth respectively

= v_{p} = \frac{2 G M _{p}}{R _{p}}

(planet) .....(i)
Given

M_{p} = 1000 M_{e},

R_{p} = 10 R_{e}

= \frac{v _{p}}{v _{e}} = \frac{2 G \times 1000 M _{e}}{10 R _{e}} \times \frac{R _{e}}{2 G M _{e}}

= v_{p} = 10 v_{e}

= v_{p} = 10 \times 11.2

= v_{p} = 112 km s^{- 1}

Q. The escape velocity from earth is 11.2kms−1. Another planet is having mass 1000 times and radius 10 times that of the earth, then escape velocity at that planet will be:

11.2 km/s

112 km/s

1.12 km/s

1120 km/s

Q. The escape velocity from earth is $11.2 km s^{- 1}$ . Another planet is having mass $1000$ times and radius $10$ times that of the earth, then escape velocity at that planet will be: