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 (g = 10 m s- 2) is:-

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 (g = 10 m s- 2) is:- (A) 20kg (B) 10kg (C) 5kg (D) 40kg

Tardigrade Admin · Accepted Answer

Fext . =m(d v/d t)-urel(d m/d t) Here, Fext .=-mg and (d v/d t)=0 ∴ mg=urel(d m/d t) or (d m/d t)=(mg/urel)=(4000 g/1000)=4g=4× 10=40kg.

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

$20 k g$

$10 k g$

$5 k g$

$40 k g$

$F_{e x t .} = m \frac{d v}{d t} - u_{re l} \frac{d m}{d t}$
Here, $F_{e x t .} = - m g$ and $\frac{d v}{d t} = 0$
$∴ m g = u_{re l} \frac{d m}{d t}$
or $\frac{d m}{d t} = \frac{m g}{u _{re l}} = \frac{4000 g}{1000} = 4 g = 4 \times 10 = 40 k g .$

Q. 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 (g=10ms−2) is:-

20kg

10kg

5kg

40kg