Question

A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth, maximum height attained by the body from the surface of the earth is

• A. R/6
• B. R/3
• C. 2R/3
• D. R

Answer 1

Answer: (B)

R/3

Answer 2

Applying conservation of mechanical energy,
$\frac{1}{2} m\left(\frac{v_{e}}{2}\right)^{2}=\frac{m g h}{1+\frac{h}{R}}$
or $\frac{v_{e}^{2}}{8}=\frac{g h}{1+\frac{h}{R}}$
?? $\frac{2 g R}{8}=\frac{g h}{1+h / R} \ldots$ (i)
$\left(\because v_{e}=\sqrt{2 g R}\right)$
On solving E (i), we get $h=\frac{R}{3}$.