Question

A $4000kg$ rocket is set for firing. If the exhaust speed is $1000ms^{- 1},$ the mass to be ejected per second to just overcome gravitational pull $\left(g = 10 m s^{- 2}\right)$ is:-

• A. $20kg$
• B. $10kg$
• C. $5kg$
• D. $40kg$

Answer 1

Answer: (D)

$F_{ext . }=m\frac{d v}{d t}-u_{rel}\frac{d m}{d t}$
Here, $F_{ext .}=-mg$ and $\frac{d v}{d t}=0$
$\therefore mg=u_{rel}\frac{d m}{d t}$
or $\frac{d m}{d t}=\frac{mg}{u_{rel}}=\frac{4000 g}{1000}=4g=4\times 10=40kg.$