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Correct option is C)

Let $R$ be the radius of Earth and $m$ be the mass of the rocket.

At the altitude $4R $ from surface of Earth:

Let $v$ be the total speed of the rocket at that altitude of $4R $. This speed is inclusive of the angular velocity of Earth's rotation and due to the propelling engine.

$K.E=21 mv_{2}$

$P.E=−(1.25R)GMm $

While the object is inside the Earth's gravitational field, the total energy is negative. For the rocket to escape the Earth's gravitational field, the total energy must be 0 or more. Then at infinite distance the energy of the rocket will be 0 or more. So it will not come back towards Earth.

$21 mv_{2}=(1.25R)GMm $

$v=R2GM ×0.8 $

$=11.2km/sec×0.9≈10km/s$

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