A satellite of mass `m` is orbiting the earth in a cicular orbit of radius `r`. It starts losing its mechanical energy due to small air resistance at the rate of `k` joule/sec. The time taken by the satellite to hit the suface of the earth is (`M` and `R` are the mass and radius of the earth)

Options

A. `(GMm)/K(1/R-1/r)`
B. `(GMm)/(2K)(1/R-1/r)`
C. `(2GMm)/K(1/R-1/r)`
D. `(GMm)/K(1/R+1/r)`

Answer

B

Explanation

`F.v=kimpliesm.(dv)/(dt).v=k`
`int_(0)^(t) dt=m/k int_(v_(i))^(v_(t)) vdv=m/(2k)((6M)/R-(6M)/r)`
`t=(6Mm)/(2k)(1/R-1/r)`