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Q.

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 30° with the line joining the centre of the Earth and point A, as shown. Find the speed V2 of particle (in km/s) if particle passes grazing the surface of the earth. Consider gravitational interaction only between these two …up to two decimal places (use GMR=64×106 m2/s2 )

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answer is 5.66.

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Detailed Solution

Using conservation of angular momentum:mv1cos⁡60∘4R=mv2R⇒v2v1=2 …..(1)By conservation of energy system−GMm4R+12mv12=−GMmR+12mv22⇒12v22−12v12=34GMR⇒v1=1264×106=80002 m/s=5.66 km/s
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