# Doubt from Gravitation

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Ans is B?

Don't know the answer , bro post solution

Total energy of circular path \frac{-GMm}{3R}
Total energy of ellipise \frac{-GMm}{2R}
Take diff.
ΔT. E= \frac{-GMm}{6R}

Total energy of parabolic orbit is zero
Total energy of elliptical orbit is -GMm/2a where 'a' is semi major axis

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There is two values of a
a=R or a=3R

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I did it like this

Also some analysis
When the particle moves close to the surface of the earth it speed is at its Max.

Why u are taking circular orbit ? It is given parabolic path initially

Circular path gives us the energy that is required to not be in an ellipse

That initial condition is given so that you can understand the course of motion.

Well just got the answer it's B and C

Intially as the path is parabolic so energy is 0
Then it will follow the elliptical path that's energy will be \displaystyle \frac{-GMm}{2a} where a=R so the diff. Will be C
For only first rotation after that B will be the difference.
For first rotation
a(e+1)=\frac{3R}{2} (aphelion)