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A satellite in force free space sweeps stationary interplanetary dust at a rate dM/dt = αv where M is the mass and v is the velocity of the satellite and α is a constant. What is the deceleration of the satellite?

1. -αv²
2. -αv²/2M
3. -αv²/2M
4. -2αv²/M

Correct answer: -αv²/2M

Solution

The rate of change of momentum of the satellite due to the accumulation of dust is equal to the force causing deceleration. Using the relation F = dp/dt and substituting dM/dt = αv, we derive the deceleration as -αv²/2M.

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