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A particle is projected from point A, th...

A particle is projected from point `A`, that is at a distance `4R` form the centre of the earth, with speed `V_(1)` in a direction making `30^(@)` with the line joining the centre of the earth and point `A`, as shown. Consider gravitational interaction only between thesetwo. (Use `(GM)/R=6.4xx10^(7) m^(2)//s^(2)`). The speed `V_(1)` if particle pasess grazing the surface of the earth is

A

(a)`(8000)/(sqrt(2))`

B

(b)`800`

C

(c)`800sqrt(2)`

D

(d)None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Conserving angular momentum `:m(v_(1)cos60^(@))4R=mv_(2)Rimplies(v_(2))/(v_(1))=2`
Conserving energy of the system `:(GMm)/(4R)+(1)/(2)mv_(1)^(2)=(GMm)/(R)+(1)/(2)mv_(2)^(2)`
`implies(1)/(2)v_(2)^(2)-(1)/(2)v_(1)^(2)=(3)/(4)(GM)/(R)impliesv_(1)^(2)=(1)/(2)(GM)/(R)impliesv_(1)=(1)/(sqrt(2))sqrt(64xx10^(6))=(8000)/(sqrt(2))m//s`
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