Question

A satellite moving with velocity v in force free space collects stationary interplanetary dust at a rate of dM/dt=av where M is mass of (satellite+dust) at that instance. The instantaneous acceleration of the satellite is: (here ' a ' is actually ' alpha ' (as i was unable to write 'alpha' on system) which I think is a constant)

(-2av2​)​​​​/M

(-av2)/M​

(-av2)/2M​​

-av2​

Answer 1

hello friend..!!

it is given that ,$\frac{dM}{dt}$ = av 

to find instantaneous accelaration ,

F = $\frac{d}{dt}$(mv)

⇒ F = m $\frac{dv}{dt}$ + v$\frac{dm}{dt}$

⇒ F = m$\frac{dv}{dt}$ + v(av)

since we know F = 0 

therefore,

m$\frac{dv}{dt}$ = - av² 

⇒ $\frac{dv}{dt}$  = - av² / m .

therefore the instantaneous accelaration is -av²/m .

--------------------------------------------

hope it is useful...!!

Answer 2

For variable mass problems force=

F=(DM/Dt)v

now dM/dt=αv substituting in above we get

F=αv2

∴ Retardation=-F / M=- αv2 / M