A satellite of mass ‘m’ is orbiting a planet of mass M in a circular orbit of radius R. The satellite changes its orbit by expelling small amount of fuel [5% of its existing mass ] with high speed U in a direction opposite to the direction of its orbital velocity. Find Umax (approximately) of the expelled mass for which, satellite cannot escape the gravitational field of planet.
see full answer
Your Exam Success, Personally Taken Care Of
1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
An Intiative by Sri Chaitanya
a
GMR1/2
b
5GMR1/2
c
7GMR1/2
d
3GMR1/2
answer is C.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
Detailed Solution
V0=GMR Binding energy =GMm2RIf Ve is escape speed, then12mVe2=12mV02+GMm2R⇒Ve=2GMR1/2=2V0Using conversation of momentum;mV0=(m−Δm)Ve−ΔmUmax⇒mV0=m−5100m2V0−5m100Umax Umax=(2×95−100)5V0≈7V0