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. $\frac{R}{(\frac{gR}{2V^2}-1)}$
• B. $R(\frac{gR}{2V^2}-1)$
• C. $\frac{R}{(\frac{2gR}{V^2}-1)}$
• D. $R(\frac{2gR}{V^2}-1)$

Answer 1

The correct option is C

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

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

$\Rightarrow \frac{1}{2}M{V}^2=G{M}_{e}M(\frac{1}{R}-\frac{1}{R+h})....\left(i\right)$

Also $g=\frac{G{M}_e}{R^2}.....\left(2\right)$

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