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A Rocket having initial mass 5xx10^(6)kg...

A Rocket having initial mass `5xx10^(6)kg` , which include mass of fuel of mass `4xx10^(6)kg` is ejecting gas with velocity `4000m//s` relative to Rocket. Then what will be the velocity of rocket when entire fuel finishes?

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`V=u_("rec").ln((m)/(M))`
`V=400 ln(5)`
`V=6439.75m//s`
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