The first & second stage of two stage rocket separately weigh 100 kg and 10 kg and contain 800kg and 90kg fuel respectively. If the exhaust velocity of gases is 2 km/sec then find velocity of rocket (nearly) (`log_(10)5=0.6990`) (neglect gravity)

Explanation

`V=V_(0)+2.3` ulog `(m_(0)//m)`
Velocity as the first stage is detached `= V_(0)`
`V_(0)=2.3` ulog `(m_(0)//m)`
`=2.3xx2xx10^(3)xx log(1000//200)`
`=2.3xx2xx0.699xx10^(3)=3.2xx10^(3)`
Velocity acquired with second stage = V
`V=V_(0)+2.3u log(m_(0)//m)`
`=3.2xx10^(3)+2.3xx2xx10^(3)xx log(100//10)`
`=3.2xx10^(3)+4.6xx10^(3)=7.8xx10^(3)m//s`