Question

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be: (Take radius of earth $=6400km$ and $g=10m{s}^{-2}$ )

• A. 800 km
• B. 1600 km
• C. 2133 km
• D. 4800 km

Answer 1

Answer: (A)

$v_e=\sqrt{\frac{2Gm}{R}}$
$\frac{-GMm}{R}+\frac{1}{2}m\frac{V_e^2}{9}=-\frac{GMm}{R+h}$
$\frac{GM}{R+h}=\frac{GM}{R}-\frac{V_e^2}{18}$
$\frac{GM}{R+h}=\frac{GM}{R}-\frac{GM}{9R}$
$\frac{GM}{R+h}=\frac{8GM}{9R}$
$\frac{1}{R+h}=\frac{8}{9R}$
$9R=8R+8h$
$h=\frac{R}{8}\Rightarrow \frac{6400}{8}\Rightarrow 800km$