First slide

Gravitational potential and potential energy

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

Moderate

A

$R / (\frac{gR}{2 V^{2}} - 1)$
B

$R (\frac{gR}{2 V^{2}} - 1)$
C

$R / (\frac{2 gR}{V^{2}} - 1)$
D

$R (\frac{2 gR}{V^{2}} - 1)$

Solution

$\begin{array}{l} ΔK . E . = ΔU \\ \Rightarrow \frac{1}{2} {MV}^{2} = {GM}_{e} M (\frac{1}{R} - \frac{1}{R + h}) . . . . . . . (i) \end{array}$
$Also g = \frac{{GM}_{e}}{R^{2}} . . . . . . . . . (ii)$
On solving (i) and (ii) $h = \frac{R}{(\frac{2 gR}{V^{2}} - 1)}$

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