Question

An object is released from rest at a distance of ${2r}_e$ from the center of the Earth, where $r_e$ is the radius of the Earth. Find out the velocity of the object when it hits the Earth in terms of the gravitational constant $\left(G\right)$, the mass of the Earth $\left(M\right)$, and $r_e$.

• A. $\sqrt{GM/r_e}$
• B. $GM/r_e$
• C. $\sqrt{GM/2r_e}$
• D. $GM/2r_e$
• E. $2GM/r_e$

Answer 1

The correct option is A $\sqrt{GM/r_e}$

Given:

Initial velocity, $u=0$ , $h=2r_e$

Now, by using: $v^2=u^2+2gh$

$v^2=0+2g\times 2r_e$

By putting $g=GM/{r_e}^2$ in above equation

We get, $v^2=2GM/{r_e}^2\times 2r_e$

$v^2=GM/2r_e$

$v=\sqrt{GM/2r_e}$