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7.Gravitation
normal
A geostationary satellite is orbiting the earth at a height of $6\, R$ from the earth’s surface ($R$ is the earth’s radius ). What is the period of rotation of another satellite at a height of $2.5\, R$ from the earth’s surface
A
$6\sqrt 2 \,hours$
B
$10\, hours$
C
$\frac{{5\sqrt 5 }}{{\sqrt 3 }}\,hours$
D
none of the above
Solution
$T = 2\pi \sqrt {\frac{{{r^3}}}{{GM}}} $
$\therefore {\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^2} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^3} = {\left( {\frac{{6R + R}}{{2.5R + r}}} \right)^3} = 8$
${T_2} = \frac{{{T_1}}}{{\sqrt 8 }} = \frac{{24}}{{\sqrt 8 }} = 6\sqrt 2 h\,r$
Standard 11
Physics
