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7.Gravitation
normal
A satellite moving with velocity $v$ in a force free space collects stationary interplanetary dust at a rate of $\frac{{dM}}{{dt}} = \alpha v$ where $M$ is the mass (of satellite + dust) at that instant . The instantaneous acceleration of the satellite is
A
$ - \frac{{\alpha {v^2}}}{{2M}}$
B
$ - \frac{{\alpha {v^2}}}{{M}}$
C
$ - \alpha {v^2}$
D
$ - \frac{{2\alpha {v^2}}}{{M}}$
Solution
${a_{inst}} = \frac{{\alpha {V^2}}}{M}$
$F=\frac{d}{d t}(m v) =m \frac{d v}{d t}+v \frac{d m}{d t}$
$=m \frac{d v}{d t}+v(a v)$
since $\mathrm{F}=\mathrm{O}$
$m \frac{d v}{d t}=-v(a v)$
$\frac{d v}{d t}=a=-\frac{a v^{2}}{m}$
Standard 11
Physics
