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4.1 , newtons laws of motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics4.1 , newtons laws of motion1 Mark
MCQ
A satellite in force-free space sweeps stationary interplanetary dust at a rate $\frac{d M}{d t}=\alpha v$ where $M$ is the mass, $v$ is the velocity of the satellite and $\alpha $ is a constant. What is the deacceleration of the satellite
  • A
    $ - 2\alpha {v^2}/M$
  • B
    $ - \alpha {v^2}/2M$
  • ✓
    $ - \alpha {v^2}/M$
  • D
    $ - \alpha {v^2}$
✓

Answer

Correct option: C.
$ - \alpha {v^2}/M$
c
The force acting on the satellite is given by

$F =\frac{ d }{ d t }( M v )$

$F=\frac{ dv }{ dt } M + v \frac{ dM }{ dt }$

$F= M \frac{ dv }{ dt }+ v (\alpha v )$

We know that the net force is zero. $F =0$,

$M \frac{ d v }{ dt }=- v (\alpha v )$

$\frac{d v}{d t}=a=-\frac{\alpha v^{2}}{M}$

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