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 Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become 32  times larger. Due to this the farthest distance from the center of the earth that the satellite reaches is R. Value of R is :

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a

4Re

b

2Re

c

25Re

d

3Re

answer is D.

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Detailed Solution

Ei=-GMm2ReAfter supplying kinetic energy,Ef=-GMm2Re+12 m32GMRe2Ef=-GMm2Re+12 m32GMRe=-GMm4ReLet say a is semimajor axis of new orbit.Ef=-GMm2a   ⇒-GMm4Re=-GMm2a   ⇒2a=4Re We know that major axis can be given as, 2a=rmin+rmax ⇒4Re=Re+rmax  ⇒rmax=3Re
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