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  4. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius R e . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that is become √(3/2) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R , value of R is :

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Q. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius $R _{ e }$. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that is become $\sqrt{\frac{3}{2}}$ times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is $R ,$ value of $R$ is :

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Solution:

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$V _{0}=\sqrt{\frac{ GM }{ R _{ e }}}$
$\frac{- GMm }{ R _{ e }}+\frac{1}{2} mv ^{2}=\frac{- GMm }{ R _{\max }}+\frac{1}{2} mv ^{\prime 2}$... (i)
$VR _{ e }= V ^{\prime} R _{\max }$...(ii)
Solving (i) $\&$ (ii)
$R _{\max }=3 R _{ e }$