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Question

Find the mass (m) of the rocket as a function of time, if it moves with a constant acceleration a in the absence of external force. The gas escapes with a constant velocity u relative to the rocket and its initial mass was m0.

A
m=m0eat/u
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B
m=m0et/u
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C
m=m0eat/u
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D
m=m0e2at/u
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Solution

The correct option is A m=m0eat/u

Since Fext=0, we get
Fnet=Vr(dmdt)=udmdt ... (I)
Also Fnet=ma ...(II)

By eq. (I) and (II)
ma=udmdt
Integrating,
mm0dmm=t0a dtu
[lnmm0]=atu
mm0=eat/u
m=m0eat/u

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