Solution :
We know that :
Formula for Gravitational force is given by :
[tex]$F_g=\frac{Gmn}{r^2}$[/tex]
where, G is the gravitational constant
M is the mass of the bigger body
m is the mass of the smaller body
r is the distance between the two bodies.
And the formula for the centripetal force is given by :
[tex]$F_c=\frac{mv^2}{r}$[/tex]
where, m is the mass of the rotating body
v is the velocity
r is the radius of rotation of the body.
We know that mathematically, the gravitational force is equal to the centripetal force of the body.
Therefore,
[tex]$F_g=F_c$[/tex]
[tex]$\frac{GMm}{r^2}=\frac{mv^2}{r}$[/tex]
[tex]$\sqrt{\frac{GM}{r}}=v$[/tex]
Hence derived.
