Question

A particle falls from infinity to the earth. Its velocity on reaching earth of radius R, is:

• A. $2Rg$
• B. $Rg$
• C. $\sqrt{Rg}$
• D. $\sqrt{2Rg}$

Answer 1

The correct option is D $\sqrt{2Rg}$

P.E at infinity is zero and K.E is also zero as the particle starts from rest at infinity.

Using conservation of mechanical energy at the surface of earth and at infinty, $K.E_R+P.E_R=0$

$\frac{1}{2}m{v}^2+(-\frac{GMm}{R})=0$ where $GM=g{R}^2$

$⟹v=\sqrt{2gR}$