Question

An object is propelled vertically to a maximum height of 4R from the surface of a planet of radius R and mass M. The speed of object when it returns to the surface of the planet is.

• A. $2\sqrt{\frac{2GM}{5R}}$
• B. $\sqrt{\frac{GM}{2R}}$
• C. $\sqrt{\frac{3GM}{2R}}$
• D. $\frac{GM}{5R}$

Answer 1

The correct option is A $2\sqrt{\frac{2GM}{5R}}$

Using Energy conservation

$\frac{-GMn}{5R}+0=\frac{-GMm}{R}+\frac{1}{2}m{v}^2$
$V=2\sqrt{\frac{2GM}{5R}}$