A rocket is moving with constant acceleration `omega` . Assume external forces on it to be zero . Exhaust gases escape with velocity u relative to the rocket . Find how its mass changes with time if its initial mass is `m_(0)`.

Explanation

`F=d/(dt) (-Mu)--u(dM)/(dt)` (since u is constant)
`:. Momega =-u(dM)/(dt)` ( where `omega` is its acceleration )
`(dM)/M =(-domega)/u`
Integrating `log M =-omega/ut+C`
when `t=0, M=M_(0)`
so `C=log M_(0), log M=-omega/ut+log M_(0) :. log M/M_(0)= - omega/ut`
`M/M_(0)=e^(-omega/ut) "or" M= M_(0)e^(-omega/ut)`
Thus , the mass of the rocket changes exponentially