1.

A satellite in force free space sweeps stationary interplanetary dust at a rate of dM//dt=alphav, where M is mass and v is the speed of satellite and alpha is a constant. The acceleration of satellite is

Answer»

`(-alpha v^(2))/(2M)`
`-alpha v^(2)`
`(-2alpha v^(2))/(M)`
`(-alpha v^(2))/(M)`

Solution :Rate of change of MASS `(dM)/(dt)=alphav`
Retarding force=Rate of change of momentum
`="Velocity"xx" Rate of change in mass"=-VXX(dM)/(dt)`
`=-vxxalpha v=-alphav^(2)`. (MINUS sign of v due to deceleration) THEREFORE deceleration `=-(alphav^(2))/(M)`.


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