A satellite in force free space sweeps stationary interplanetary dust at a rate d M / d t=α v, where M is the mass, v is the velocity of the satellite and α is a constant. What is the deacceleration of the satellite?

Question

A satellite in force free space sweeps stationary interplanetary dust at a rate d M / d t=α v, where M is the mass, v is the velocity of the satellite and α is a constant. What is the deacceleration of the satellite? (A) -2 α v2 / M (B) -α v2 / M (C) +α v2 / M (D) -α v2

Tardigrade Admin · Accepted Answer

F=(d p/d t)=v((d m/d t)) =α v2 ∴ a =(F/M) =(α v2/M)

Q. A satellite in force free space sweeps stationary interplanetary dust at a rate $d M / d t = αv$ , where $M$ is the mass, $v$ is the velocity of the satellite and $α$ is a constant. What is the deacceleration of the satellite?

$- 2 α v^{2} / M$

$- α v^{2} / M$

$+ α v^{2} / M$

$- α v^{2}$

$F = \frac{d p}{d t} = v (\frac{d m}{d t}) = α v^{2}$
$∴ a = \frac{F}{M}$
$= \frac{α v ^{2}}{M}$

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

−2αv2/M

−αv2/M

+αv2/M

−αv2