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

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Solution

The correct option is C

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

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The correct option is C △K.E.=△U ⇒12MV2=GMeM(1R−1R+h)....(i) Also g=GMeR2 On solving (i) and (ii) h=R(2gRV2−1)

The correct option is C

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