Q. 463.7( 3 Votes )

A rocket accelera

Answer :

At time t,


Kinetic energy


Now at time t+Δt,


Rocket loses mass Δm and gains velocity Δv and releases gas with relative velocity of u


Velocity of rocket w.r.t ground


Velocity of gas w.r.t ground


total kinetic energy of the system w.r.t ground




[neglecting terms with as both of them are very small]



Kinetic gained in Δt interval,





----(1)


there is no external force internal forces must cancel out,






Putting the above in equation (1), we get,






By work energy theorem,


Work done = change in kinetic energy


W


the device that ejects gas does work = ∆m u2 in this time interval


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