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7.Gravitation
normal
A satellite in force free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t}=\alpha v$ where $M$ is mass and $v$ is the speed of satellite and $\alpha$ is a constant. The acceleration of satellite is
A
$\frac{-\alpha v^{2}}{M}$
B
$-\alpha v^{2}$
C
$\frac{-2 \alpha v^{2}}{M}$
D
$\frac{-\alpha v^{2}}{2 M}$
Solution
Rate of change of mass $\frac{d M}{d t}=\alpha v$.
Retarding force $=$ Rate of change of momentum
$=$ Velocity $\times$ Rate of change in mass $=-v \times \frac{d M}{d t}$
$=-v \times \alpha v=-\alpha v^{2} .$ (Minus sign of $v$ due to deceleration)
Acceleration $=-\frac{\alpha v^{2}}{M} .$
Standard 11
Physics