A rocket of mass M is launched vertically from the surface …

Physics Gravitation Mix Single Correct MCQ

Published on: September 13, 2026

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

$R/\left(\frac{gR}{2v^{2}}-1\right)$

$R\left(\frac{gR}{2v^{2}}-1\right)$

$R/\left(\frac{2gR}{v^{2}}-1\right)$

$R\left(\frac{2gR}{v^{2}}-1\right)$

Text Solution

Verified by Experts

The correct answer is:

$\Delta K . E . = \Delta U$

$\Rightarrow \frac{1}{2}MV^{2} = GM_{e}M \left( \frac{1}{R} - \frac{1}{R+h} \right)$ …(i)

Also $g = \frac{GM_{e}}{R^{2}}$ …(ii)

On solving (i) and (ii) $h = \frac{R}{\left(\frac{2gR}{v^2} - 1\right)}$

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