GATE_AE_2027_MOCK_02_Q58 GATE 2027 Aerospace Engineering All-India Master Mock 02 (Compressible Aerodynamics & High-Speed Propulsion) NAT · 2 Marks
Propulsion • Rocket Propulsion • Solid, Liquid & Hybrid Rocket Engines

A liquid rocket engine burns propellant producing thrust $F = 150\text{ kN}$ at a total propellant mass flow rate $\dot{m} = 50\text{ kg/s}$. What is the specific impulse $I_{sp}$ (in seconds)? (Take standard gravitational acceleration $g_0 = 9.81\text{ m/s}^2$, round to one decimal place).

Answer Key:
305.8

Step-by-Step Verified Solution

### Solution: $I_{sp} = \frac{F}{\dot{m} g_0} = \frac{150000}{50 \times 9.81} = \frac{3000}{9.81} \approx 305.81 \approx 305.8\text{ s}$. Correct: 305.8 (range 304.5 to 307.0).
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