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# A geostationary satellite is at a height h above the surface of the earth If R is radius of earth 1) The mimimum coaltitude on earth upto which the satellite can be used for communication is $\sin ^{-1} \bigg(\large\frac{R}{R+a}\bigg)$ 2) The maximum coaltitude on earth upto which the satellite can be used for communication is $\sin ^{-1} \bigg(\large\frac{R}{R+h}\bigg)$ 3) Area of earth escaped from this satellite is given by $(2 \pi R^2(1+\sin \theta)$ 4) Area of earth escaped from this satellite is given by $(2 \pi R^2(1+\cos \theta)$

a) 1 and 4 b) 1 and 3 c) 1,2 and 3 d) 2 and 3

From diagram $\sin \theta=\large\frac{R}{R+h}$
minimum coaltitude $=\sin ^{-1} \bigg(\large\frac{R}{R+h}\bigg)$
The curved area AB on earth $=2 \pi R^2 (1-\sin \theta)$
Area on earth escaped from satellite $4 \pi R^2 - 2 \pi R^2 (1-\sin \theta)$
$\qquad= 2 \pi R^2 (1+\sin \theta)$
Hence d is the correct answer.

edited Feb 17, 2014 by meena.p