For a rocket propulsion velocity of exhaust gases relative to rocket is 2 km / s. If mass of rocket system is 1000 kg, then the rate of fuel consumption for a rocket to rise up with acceleration 4.9 m / s 2 will be :

Question

For a rocket propulsion velocity of exhaust gases relative to rocket is 2 km / s. If mass of rocket system is 1000 kg, then the rate of fuel consumption for a rocket to rise up with acceleration 4.9 m / s 2 will be : (A) 12.25 kg / s (B) 17.5 kg / s (C) 7.35 kg / s (D) 5.2 kg / s

Tardigrade Admin · Accepted Answer

Here, thrust = v ( dm / dt )=(2000) ( dm / dt ) For rocket, v ( dm / dt )= m ( g + a ) ⇒ 2000 ( dm / dt )=1000(9.8+4.9) ⇒ ( dm / dt )=7.35 kg / s

Q. For a rocket propulsion velocity of exhaust gases relative to rocket is $2 km / s$ . If mass of rocket system is $1000 k g$ , then the rate of fuel consumption for a rocket to rise up with acceleration $4.9 m / s^{2}$ will be :

$12.25 k g / s$

$17.5 k g / s$

$7.35 k g / s$

$5.2 k g / s$

Here, thrust $= v \frac{d m}{d t} = (2000) \frac{d m}{d t}$
For rocket, $v \frac{d m}{d t} = m (g + a)$
$\Rightarrow 2000 \frac{d m}{d t} = 1000 (9.8 + 4.9)$
$\Rightarrow \frac{d m}{d t} = 7.35 k g / s$

Q. For a rocket propulsion velocity of exhaust gases relative to rocket is 2km/s. If mass of rocket system is 1000kg, then the rate of fuel consumption for a rocket to rise up with acceleration 4.9m/s2 will be :

12.25kg/s

17.5kg/s

7.35kg/s

5.2kg/s