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Impulsive Forces in Collision

For a Rocket ...

Question

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

12.25 k g / s

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17.5 k g / s

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7.35 k g / s

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5.2 k g / s

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Solution

The correct option is C $7.35 k g / s$
Relative velocity of exhaust gas $V = 2 k m / s = 2000 m / s$
Thrust force $F_{t} = V \frac{d m}{d t} = 2000 \times \frac{d m}{d t}$
Acceleration $a = 4.9 m / s^{2}$
Mass of rocket $M = 1000 k g$
Using $M a = F_{t} - M g$
Or $1000 \times 4.9 = 2000 \times \frac{d m}{d t} - 1000 \times 10$
$⟹ \frac{d m}{d t} = 7.35 k g / s$
So, option C is correct.

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