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GATE 2021 AE – Question 18

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

A rocket produces 25 MN thrust for 150 s with specific impulse 2980 N s/kg. Propellant consumed is approximately

  1. 8390 kg
  2. 82300 kg
  3. $1.26\times10^6$ kg
  4. $11.2\times10^6$ kg

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Correct answer: (C) $1.26\times10^6$ kg

Explanation

**Specific impulse** relates the thrust $F$ to the propellant weight or mass flow. In this question $I_{sp}$ is given as 2980 N·s per kg of propellant:
$$I_{sp}=\frac{F}{\dot m_p}\;\Rightarrow\;\dot m_p=\frac{F}{I_{sp}} .$$

**Mass consumed** in time $t$:
$$m_p=\dot m_p\,t=\frac{F\,t}{I_{sp}}=\frac{25\times10^6\times150}{2980}=\frac{3.75\times10^9}{2980}=1.258\times10^6\text{ kg}.$$

Answer **$1.26\times10^6$ kg** (C).