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

1. −2αv
2. −αv²
3. −αv²/2M
4. −αv²

Correct answer: −αv²/2M

Solution

The satellite's acceleration can be derived using the principle of conservation of momentum. The rate of change of momentum due to the dust is proportional to the mass swept per unit time, leading to the acceleration being proportional to −αv²/2M.

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