Question

A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$. Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

• A. $R /\left(\frac{g R}{2 V^{2}}-1\right)$
• B. $R\left(\frac{g R}{2 V^{2}}-1\right)$
• C. $R /\left(\frac{2 g R}{V^{2}}-1\right)$
• D. $R\left(\frac{2 g R}{V^{2}}-1\right)$

Answer 1

Answer: (C)

$\Delta K . E .=\Delta U$
$\Rightarrow \frac{1}{2} M V^{2}=G M_{e} M\left(\frac{1}{R}-\frac{1}{R+h}\right)$ ...(i)
Also $g=\frac{G M_{e}}{R^{2}}$ ...(ii)
On solving (i) and (ii),
$h=\frac{R}{\left(\frac{2 g R}{V^{2}}-1\right)}$