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`        An artificial satellite (of mass m) of the earth (radius R and mass M) moves in an orbit whose radius in n times the radius of the earth. Assuming resistance to the motion to be proportional to e square velocity, that is, F=av^2 , find how long the satellite will take to fall onn to the earth.`
7 years ago

25 Points
```										Dear Aditya
initial radiusof the orbit of satellite is nR
here the gravitation pull of the earth provides the necessary centripital force
hence GMm/r2 =mv2/r  where r is the radius of the orbit of satellite at any time and v is the velocity.
hence v=√GM/r
it is given that resistance to motion of satellite issgiven by F=av2
so F=mdv/dt
hence av2=mdv/dt
integrating with limits of t varying from o to T and that of v varying from √GM/nR to √GM/R
m(√nR/GM -√R/GM)=aT
T=m/a*√R/GM*(√n-1)

Good Luck
Abhinav Batra

```
7 years ago
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