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GATE 2026 AE – Question 39

Propulsion · Rockets: thrust equation, specific impulse, multi-staging, solid and liquid propellant rockets · 2 marks · Multiple choice

An ideal rocket has characteristic exhaust velocity of 1200 m/s, mass flow rate of 75 kg/s, thrust coefficient of 1.5, and nozzle throat area of 0.025 m$^2$. The chamber pressure in kPa and the specific impulse due to gravity in seconds are ________, respectively. Assume that the acceleration due to gravity is 9.8 m/s$^2$.

  1. 3600 and 183.67
  2. 4600 and 190.51
  3. 3600 and 175.23
  4. 3500 and 183.67

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Correct answer: (A) 3600 and 183.67

Explanation

The characteristic velocity is $c^* = \frac{p_c A_t}{\dot m}$, so $p_c = \frac{1200 \times 75}{0.025} = 3.6 \times 10^6$ Pa = 3600 kPa. The specific impulse is $I_{sp} = \frac{C_F c^*}{g} = \frac{1.5 \times 1200}{9.8} = 183.67$ s.