GATE_AE_2027_MOCK_02_Q30 GATE 2027 Aerospace Engineering All-India Master Mock 02 (Compressible Aerodynamics & High-Speed Propulsion) NAT · 1 Mark
Propulsion • Rocket Propulsion • Tsiolkovsky Rocket Equation & Multistage Rockets

A rocket stage has an initial mass $m_0 = 10000\text{ kg}$ and burnout mass $m_b = 2000\text{ kg}$. If the effective exhaust velocity is $c = 3000\text{ m/s}$, what is the ideal velocity increment $\Delta v$ (in m/s) in gravity-free space? (Take $\ln 5 \approx 1.6094$, round to nearest integer).

Answer Key:
4828

Step-by-Step Verified Solution

### Solution: $\Delta v = c \ln(m_0/m_b) = 3000 \times \ln(10000/2000) = 3000 \times \ln 5 = 3000 \times 1.60944 = 4828.3 \approx 4828\text{ m/s}$. Correct: 4828 (range 4820 to 4835).
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