A satellite revolving around earth in a circular orbit of radius 4R. Due to ejection of a rocket the speed of satellite is reduced to half as a result of which satellite starts falling toward earth. Find the angle at which it will hit the earth surface.
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a
θ=37o
b
θ=33o
c
θ=40o
d
θ=32o
answer is A.
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Detailed Solution
with respect to earth, we conserve energy and angular momentumm v24R=m(v1cosθ)R2GM4R=v1cosθ ……..(1) [by conservation of angular momentum ]12m(v/2)2−GMem4R=12mv12−GM1mR ………(2)v1=54GMRfrom (i) GMR=54GMRcosθcosθ=4/5⇒θ=37∘
A satellite revolving around earth in a circular orbit of radius 4R. Due to ejection of a rocket the speed of satellite is reduced to half as a result of which satellite starts falling toward earth. Find the angle at which it will hit the earth surface.