A rocket of mass 20kg has 180 kg of fuel. The exhaust velocity of fuel is 1.6 km/sec. Calculate the ultimate velocity of the rocket gained, when the rate of consumption of the fuel is 2kg/sec. (neglect gravity)

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3.7 km/sec

2 km/sec

5 km/sec

10 km/sec

answer is A.

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Detailed Solution

The rocket will be accelerated due to the upthrust from the exhaust gases

$m \frac{dv}{dt} = (- u_{r}) \frac{dm}{dt}$

$\Rightarrow \int_{0}^{v} dv = - u_{r} \int_{m_{i}}^{m_{f}} \frac{1}{m} dm$

$\Rightarrow v = u_{r} \ln \frac{m_{i}}{m_{f}}$

On substituting the values we get

$v = 3.7 km / s$

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