Thank you for reporting, we will resolve it shortly
Q.
A body is projected vertically upwards with a speed of $\sqrt{\frac{G M}{R}}$ ( $M$ is mass and $R$ is radius of earth). The body will attain a height of
Gravitation
Solution:
Conserving mechanical energy at earth surface and at the maximum height attained by the body,
$P.E _{i}+ K . E _{i}= P . E _{j}+ K . E _{j} $
$-\frac{G M m}{R}+\frac{1}{2} m\left(\frac{G M}{R}\right)=-\frac{G M m}{r}+0$
$\Rightarrow -\frac{G M m}{2 R}=-\frac{G M m}{r} $
$\Rightarrow r =2 R $
$\Rightarrow R+h =2 R$
$ h = R$