Question

11. The critical velocity, v of a satellite depends upon the distance r from the centre of earth and
acceleration due to gravity g. By the method of dimension obtain expression for critical velocity. Ans:
v=Vgr​

Answer 1

Answer:

Consider a satellite of mass m revolving round the Earth at a, height 'h' above the surface of the Earth.

Let M be the mass and R be the radius of the Earth.

The satellite is moving with velocity V and the radius of the circular orbit is r=R+h. Centripetal force = Gravitational force

∴

r

Mv

c

2

=

r

2

GMm

∴v

c

2

=

r

GM

∴v

c

=

R+h

GM

This is the expression for critical velocity of a satellite moving in a circular orbit around the Earth,

We know that,

g

h

=

(R+h)

2

GM

GM=g

h

(R+h)

2

Substituting in equation (1), we get

∴v

c

=

R+h

g

h

(R+h)

2

∴v

c

=

g

h

(R+h)

where g

h

is the acceleration due to gravity at a height above the surface of the Earth.

solution