Q 1366123075.     An artificial satellite of mass `m` moves in an orbit whose radius is `n` times the radius of earth. Assuming the resistance to the motion is proportional to square of velocity ie `F = av^2` where `a` is a constant. How long will the satellite take to fall to earth. `M` - mass of earth `R-` radius of earth

A

`frac{m}{a} (frac{R}{GM}) sqrt {n-1}`

B

`frac{m}{a} sqrt{frac{R}{GM}}(sqrt n -1)`

C

`frac{m}{a} sqrt {frac{RG}{M}}(sqrt {n+1})`

D

`frac{m}{a} sqrt {frac{RG}{M}}(sqrt n-1)`

HINT

`frac{dE}{dt} = F.v`

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