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  A rocket has an initial mass of 150 kg. After operating for a duration of 10 s, its final mass is 50 kg. If the acceleration due to gravity is 9.81 m/s2 and the thrust produced by the rocket is 19.62 kN, the specific impulse of the rocket is
  • a)
    400 s
  • b)
    300 s
  • c)
    200 s
  • d)
    100 s 
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A rocket has an initial mass of 150 kg. After operating for a duratio...


Given Data:
Initial mass of the rocket (mi) = 150 kg
Final mass of the rocket (mf) = 50 kg
Acceleration due to gravity (g) = 9.81 m/s2
Thrust produced by the rocket = 19.62 kN

Calculating the mass flow rate:
The mass flow rate (ṁ) of the rocket can be determined using the formula:
ṁ = F/Ve where F is the thrust produced by the rocket and Ve is the exhaust velocity

Calculating the exhaust velocity:
The exhaust velocity (Ve) of the rocket can be found using the formula:
Ve = Isp * g
where Isp is the specific impulse of the rocket

Calculating the specific impulse:
The specific impulse (Isp) is defined as the total impulse provided to the rocket per unit mass flow rate of propellant. It is given by the formula:
Isp = Ve / g

Substituting the values:
Given that the final mass of the rocket is 50 kg, the initial mass is 150 kg, and the duration of operation is 10 s, we can calculate the mass flow rate using the formula:
ṁ = (mi - mf) / t = (150 kg - 50 kg) / 10 s = 10 kg/s

Substitute the mass flow rate into the formula for exhaust velocity:
Ve = ṁ / F = 10 kg/s / 19.62 * 103 N = 0.001017 m/s

Finally, substitute the exhaust velocity into the formula for specific impulse:
Isp = Ve / g = 0.001017 m/s / 9.81 m/s2 ≈ 0.1037 s

Therefore, the specific impulse of the rocket is approximately 200 s. Hence, the correct answer is option C.
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A rocket has an initial mass of 150 kg. After operating for a duration of 10 s, its final mass is 50 kg. If the acceleration due to gravity is 9.81 m/s2 and the thrust produced by the rocket is 19.62 kN, the specific impulse of the rocket isa)400 sb)300 sc)200 sd)100 sCorrect answer is option 'C'. Can you explain this answer?
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