Question

An object is dropped from the height h=2R on the surface of earth. Find the speed with the which it will collide with the ground by neglecting effect of air.

Answer 1

$\huge\text{\underline{\underline{Solution:}}}$


$\text{\underline{\underline{By\:law\:of\:conservation\:of\:energy,}}}$

△ KE = - △ P. E.


$\text{\underline{\underline{Now,}}}$


$\frac{1}{2} mv ^{2} = -$ ($U_{f} - U_{i}$ ) = $U_{i} - U_{f}$

$\frac{1}{2} mv ^{2} = - \frac{GMm}{3R} + \frac{GMm}{R}$

$\frac{1}{2} v^{2} = \frac{2GM}{3R}$

$v = \sqrt{ \frac{4GM}{3R} }$

$v = 2 \sqrt{ \frac{GM}{3R} }$