GravitationHard

Question

A particle is projected from point A, that is at a distance 4R from the centre of the Earth, with speed v1 in a direction making 30o with the line joining the centre of the Earth and point A, as shown. Find the speed v1 of particle (in m/s) if particle passes grazing the surface of the earth. Consider gravitational interaction only between these two. (use = 6.4 × 107 m2 / s2)

Options

A.
B.800
C.800 √2
D.None of these

Solution

Conserving angular momentum : m (v1 cos60o) 4R = mv2R ⇒ = 2
Conserving energy of the system : - = -
⇒ v22 - ⇒ ⇒ v1 = m/s

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