A satellite in force free space sweeps stationary interplanetary dust at a rate of frac{d M}{d t}=α

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7.Gravitation

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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

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