A rocket is launched with velocity 10 km/

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A rocket is launched with velocity $10\, km/s$. If radius of earth is $R$, then maximum height attained by it will be

A

$2R$

B

$3R$

C

$4R$

D

$5R$

A rocket is launched with velocity $10\, km/s$. If radius of earth is $R$, then maximum height attained by it will be

if body is projected with velocity $\mathrm{V}\left(\mathrm{V}<\mathrm{V}_{\mathrm{e}}\right)$ then height upto where it rises

$\mathrm{h}=\left[\mathrm{R} /\left\{\left(\mathrm{V}_{\mathrm{e}}^{2} / \mathrm{V}^{2}\right)-1\right\}\right]$

$=\left[\mathrm{R} /\left\{(11.2 / 10)^{2}-1\right\}\right]……………….\mathrm{V}_{\mathrm{e}}=11.2 \mathrm{km} / \mathrm{s}$

$\mathrm{h}=3.93 \mathrm{R}$

$h \approx 4 R$