A skylab of mass m,kg is first launched from surface of earth in a circular orbit of radius 2R (from

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7.Gravitation

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A skylab of mass $m\,kg$ is first launched from the surface of the earth in a circular orbit of radius $2R$ (from the centre of the earth) and then it is shifted from this circular orbit to another circular orbit of radius $3R$ . The minimum energy required to shift the lab from first orbit to the second orbit are

A

$\frac {mgR}{6}$

B

$\frac {mgR}{12}$

C

${mgR}$

D

${mgR}$

Solution

Required energy $=$ change in total energy

$=\frac{\mathrm{GMm}}{2(2 \mathrm{R})}-\frac{\mathrm{GMm}}{2(3 \mathrm{R})}$

$=\frac{\mathrm{mgR}}{12}$

Standard 11

Physics

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