A satellite moving through interplanetary dust sweeps up stationary dust at rate dM/dt=αv, where M is its mass and v its speed. Find its acceleration due to the collected dust.
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A satellite moving through interplanetary dust sweeps up stationary dust at rate dM/dt=αv, where M is its mass and v its speed. Find its acceleration due to the collected dust.

G1 Physics · Accepted Answer

Dust initially carries no momentum relative to the inertial frame. During assimilation, M dv/dt=−v(dM/dt) because the moving body transfers momentum to incoming dust. With dM/dt=αv, acceleration dv/dt=−αv²/M. Answer: D.