Question

The escape velocity from the earth's surface is 11
km/sec. If the radius of a planet is double to that of
the earth but the average density is same as that
of the earth, then the escape velocity from the
planet would be​

Answer 1

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Physics

Gravitation

Binding Energy and Satellites

The escape velocity from th...

PHYSICS

The escape velocity from the earth's surface is 11km/sec. If the radius of a planet is double to that of the earth but the average density is same as that of the earth, then the escape velocity from the planet would be:

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ANSWER

Answer is A.

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.