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7.Gravitation
normal
A geostationary satellite is at a height $h$ above the surface of earth. If earth radius is $R$
A
The minimum colatitude on earth upto which the satellite can be used for communication is $\sin^{-1} (R/R+h).$
B
The maximum colatitudes on earth upto which the satellite can be used for communication is $\sin^{-1} (R/R+h).$
C
The area on earth escaped from this satellite is given as $2\pi R^2 (1 + \sin \theta )$
D
$(A)$ and $(C)$ both
Solution
From diagram $\sin \theta=\frac{R}{R+h}$
minimum co altitude $=\sin ^{-1}\left(\frac{R}{R+h}\right)$
The curved area $A B$ on earth $=2 \pi R^{2}(1-\sin \theta)$
Area on earth escaped from satellite
$=4 \pi R^{2}-2 \pi R^{2}(1-\sin \theta)$
$=2 \pi R^{2}(1+\sin \theta)$
Standard 11
Physics
