A satellite in force free space sweeps stationary interplanetary dust at a rate of dM/dt = α v, where M is mass and v is the speed of satellite and α is a constant. The acceleration of satellite is (a) -α v²2M (b) -α v² (c) -2α v²M (d) -α v²M

Answer: (d). No external force, so momentum Mv is constant: Mdv/dt + vdM/dt = 0. M a = -v(α v) = -α v² a = -(α v²)/(M), so the answer is (d).

A satellite in force free space sweeps stationary interplanetary dust… | NEET 1994 (AIPMT)

Q27NEET 1994 · AIPMTDifficult

Impulse & Momentum Conservation

A satellite in force free space sweeps stationary interplanetary dust at a rate of $dM/dt = \alpha v$ , where $M$ is mass and $v$ is the speed of satellite and $\alpha$ is a constant. The acceleration of satellite is

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Answer: (d)

No external force, so momentum $Mv$ is constant: $M\frac{dv}{dt} + v\frac{dM}{dt} = 0$ .
$M a = -v(\alpha v) = -\alpha v^2$
$a = -\frac{\alpha v^2}{M}$ , so the answer is (d).

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Impulse & Momentum Conservation question from NEET 1994 (AIPMT)

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