UPSEE Solved Model Paper 6

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 =

1

2

mv2
Potential energy on the surface PE =

−GM

R

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
∴

1

2

mv2+

−GMm

R

= 0
Or,

1

2

mv2 =

GMm

R

v2 =

2GM

R

∴ Velocity , v = √

2GM

R

And also we know that g is acceleration at the surface of earth
And its equation on gravitation g =

GM

R2

So we can modify the equation of velocity v = √

2GM

R

×

R

R

= √

2RGM

R2

Putting the value of g =

GM

R2

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