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Q.

A satellite in a force free space sweeps stationary interplanetary dust at a rate (dM/dt) = $α$ v. The acceleration of satellite is

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a

$\frac{- α v^{2}}{M}$

b

$\frac{- 2 α v^{2}}{M}$

c

$\frac{- α v^{2}}{2 M}$

d

$- α v^{2}$

answer is B.

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Detailed Solution

Thrust on the satellite,

$F = \frac{- vdM}{dt} = - v (α v) = - α v^{2}$

Acceleration $= \frac{F}{M} = \frac{- α v^{2}}{M}$

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