Question 8: Gravitation

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

Accepted Answer

Escape velocity, $V_e=\sqrt{\frac{2 G M}{R}}$
From conservation of energy
$$ \begin{aligned} \mathrm{KE}_i+\mathrm{PE}_i & =\mathrm{KE}_f+\mathrm{PE}_f \ \frac{-G M m}{R}+\frac{1 m}{2} \frac{V_e^2}{9} & =\frac{-G M m}{R+h} \ \frac{G M}{R+h} & =\frac{G M}{R}-\frac{V_e^2}{18} \quad\left(	herefore V=\frac{V_e}{3}ight) \ \frac{G M}{R+h} & =\frac{G M}{R}-\frac{G M}{9 R} \quad\left(	herefore V_e=\sqrt{\frac{2 G M}{R}}ight) \ \frac{G M}{R+h} & =\frac{8 G M}{9 R} \ \frac{1}{R+h} & =\frac{8}{9 R} \end{aligned} $$
ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ                     $$ \begin{aligned} & R=8 h \Rightarrow h=\frac{R}{8} \ & h=\frac{6400}{8}=800 \mathrm{~km} \end{aligned} $$

Answer

2400 km

Answer

4800 km

Answer

800 km

Answer

1600 km

Gravitation

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

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