A satellite of mass m , initially at rest on earth, is launched into a circular orbit at a height eq

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7.Gravitation

hard

A satellite of mass $m$, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is

A

$\frac{{\sqrt 3 }}{4}\,mgR$

B

$\frac{1}{2}\,mgR$

C

$\frac{1}{4}\,mgR$

D

$\frac{3}{4}\,mgR$

Solution

Energy required

$=\mathrm{T} \varepsilon_{\mathrm{f}}-\mathrm{T} \varepsilon_{\mathrm{i}}=\frac{3}{4} \frac{\mathrm{GMm}}{\mathrm{R}}=\frac{3}{4} \mathrm{mgR}$

$\mathrm{T} \varepsilon_{\mathrm{f}}=-\frac{\mathrm{GMm}}{2(2 \mathrm{R})} \quad$ in orbit

$\mathrm{T} \varepsilon_{\mathrm{i}}=-\frac{\mathrm{GMm}}{\mathrm{R}} \quad$ on surface

Standard 11

Physics

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