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>>Systems of Particles and Rotational Motion
>>Linear Momentum of a System of Particles
>> $A satellite in force free space sweeps s$

Question

A satellite in force free space sweeps stationary interplanetary dust at a rate $\frac{d M}{d t} = α v$ , where $M$ is the mass and $v$ is the velocity of the satellite and $α$ is a constant. The tangential acceleration of satellite is

A

$- α v^{2}$

B

$\frac{- α v ^{2}}{2 M}$

C

$\frac{- α v ^{2}}{M}$

D

$\frac{- 2 α v ^{2}}{M}$

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Solution

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Correct option is C)

we know $F = \frac{d}{d t} (M v) = M \frac{d v}{d t} + v \frac{d M}{d t} = M \frac{d v}{d t} + v α v$ As, $\frac{d M}{d t} = α v$

since, $F = 0$ , we have acceleration $\frac{d v}{d t} = \frac{α v ^{2}}{M}$

The deceleration of the satellite. $= - \frac{α v ^{2}}{M}$
hence,option C is correct.

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