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GATE 2019 AE – Question 56

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

A rocket has initial mass 1720 kg, final dry mass 1000 kg and specific impulse 3000 N s/kg. Neglect external forces. Find the velocity increment in km/s (two decimal places).

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Correct answer: 1.60 to 1.65

Explanation

The stated N s/kg unit is impulse per propellant mass, equivalent to effective exhaust velocity 3000 m/s. Apply $\Delta v=c\ln(m_i/m_f)=3000\ln(1720/1000)=1626.97$ m/s = 1.63 km/s. Do not multiply by g again; that conversion applies when specific impulse is stated in seconds.

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