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GATE 2025 AE – Question 32

Propulsion · Rockets: thrust equation, specific impulse, multi-staging, solid and liquid propellant rockets · 1 mark · Multiple choice

An ideal two-stage rocket has identical specific impulse and structural coefficient for its two stages. For an optimized rocket, the two stages have identical payload ratio as well. The payload is 2 tons and the initial mass of the rocket is 200 tons. The mass of the second stage of the rocket (including the final payload mass) is ____ tons.

  1. 100
  2. 10
  3. 20
  4. 50

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Correct answer: (C) 20

Explanation

The overall payload ratio is $\frac{2}{200} = 0.01$. With two stages of identical payload ratio $\lambda$, $\lambda^2 = 0.01$, so $\lambda = 0.1$. The second stage, with the payload, is the mass carried by the first stage: $0.1 \times 200 = 20$ tons.