GATE_AE_2027_MOCK_05_Q52 GATE 2027 Aerospace Engineering All-India Master Mock 05 (High-Yield Comprehensive Grand Finale) NAT · 2 Marks
Flight Mechanics & Space Dynamics • Space Dynamics & Orbital Mechanics • Tsiolkovsky Rocket Equation & Multistage Rockets

A rocket in gravity-free space has effective exhaust velocity c = 2500 m/s. If the mass ratio is m_0 / m_b = 8.0, what is the velocity increment \Delta v in m/s? (Take ln 8 = 3 * ln 2 ≈ 3 * 0.69315 = 2.07944, round to nearest integer).

Answer Key:
5199

Step-by-Step Verified Solution

### Solution: \Delta v = c * \ln(m_0 / m_b) = 2500 * 2.07944 = 5198.6 ≈ 5199 m/s. Correct: 5199 (range 5190 to 5210).
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