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A satellite of mass 'M' is projected rad...

A satellite of mass 'M' is projected radially from surface of earth with speed 'u'. When is reaches a height equal to radius of earth, it ejects a rocket of mass `( M)/(10 )`and it itself starts orbiting the earth in circular path of radius 2R, find the kinetic energy of rocket.

A

`m/10(25U^(2)-(84GM)/(3R))`

B

`m/10(15U^(2)-(74 GM)/(3R))`

C

`m/8(U-sqrt((10GM)/(3R)))`

D

`m/6(25U^(2)-(94GM)/(3R))`

Text Solution

Verified by Experts

The correct Answer is:
A

`(-GMm)/R+1/2"mu"^(2)=(-TMm)/(3R)+1/2mv^(2)`….i
After ejection of rocket `impliesmV^(2)=mU^(2)-4/3(GMm)/R`
`vecP_("in"=vecP_(f)`
`impliesmv=m/5v_(2)^(2)` and `(4m)/5 v_(1)m/5v_(3)`
`v_(2)=5v" "v_(3)=4v_(1)=4sqrt((GM)/(3R))`
K.E of rocket `=1/2 m/5(v_(2)^(2)+v_(3)^(2))`
`=m/10(25v^(2)+(16 GM)/(3R))`
`=1/10(25m^(2)U^(2)-4/3(GMm)/R)+(16 GMm)/(3R)`
`=1/10(25m^(2)U^(2)-(84GMm)/(3R))`
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