Question

Calculate the escape velocity on the surface of the planet having radius 1100 km and
acceleration due to gravity on the surface of the planet is 1.6 meter per second squares.​

Please Give Full Solution​

Answer 1

Answer:

The minimum velocity with which a body must be projected up so as to enable it to just overcome the gravitational pull, is known as escape velocity.

If v

e

is the required escape velocity, then kinetic energy which should be given to the body is

2

1

mv

e

2

.

2

1

mv

e

2

=

R

GMm

⟹v

e

=

R

2GM

.

We know, Mass M = Density d * Volume V.

Volume of the earth is given as

3

4

πR

3

.

In this case, the radius of a planet is double to that of the earth but the average density is same as that of the earth.

So, v

e

=

3

8

πdGR

2

.

Therefore, escape velocity is proportional to R if density d is constant. Since the planet having double radius in comparison to earth, the escape velocity becomes twice.

That is, 11km/sec×2=22km/sec.

Hence, the escape velocity is 22km/sec.