Here, we have to find out the velocity of a principle on reaching the earth if it falls from infinity
We know that
Kinetic energy on the surface KE =
mv2 Potential energy on the surface PE =
Where:
m - mass of the particle
M - mass of the earth
v - velocity
G - universal gravitational constant
R - radius of earth
since the total enegy at infinity is zero
KE + PE = 0
∴
mv2+ = 0
Or,
mv2 =
v2 =
∴ Velocity , v =
√ And also we know that g is acceleration at the surface of earth
And its equation on gravitation g =
So we can modify the equation of velocity v =
√× =
√ Putting the value of g =
on the above equation of velocity we get
∴ Velocity v =
√2Rg That iis the velocity of a particle on reaching the earth if it falls from infinity is
√2Rg