A satellite in a force - free space sweeps stationary interplanetary dust at a rate `dM//dt = alpha v`, where `M` is the mass , `v`is the velocity of the satellite and `alpha` is a constant. What is the deacceleration of the satellite ?

Options

A. `-2 alpha v^(2)//M`
B. `-alpha v^(2)//M`
C. `+alpha v^(2)//M`
D. `- alpha v^(2)`

Answer

B

Explanation

`(dm)/(dt) = alpha v`
Since , `F = (dp)/(dt) =v (dm)/(dt) = alpha v^(2)`
`rArr a = (- alpha v^(2))/(M)`