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Mass of an empty rocket is 50 kg and mass of its fuel is 100kg. The rocket is fired on the surface of earth. If initial rate of consumption of fuel is 2 kg/s and velocity of exhaust gas relative to the body of the rocket is 800 m/s, Find the initial acceleration of the rocket

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$\frac{2}{3} m / s^{2}$

$\frac{3}{4} m / s^{2}$

$\frac{4}{5} m / s^{2}$

$\frac{5}{6} m / s^{2}$

answer is A.

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Detailed Solution

Initial thrust generated by exhaust gases

$= V_{r} \frac{dm}{dt} = 800 \times 2 N = 1600 N$

$∴$ Net upward force on the (rocket+fuel)

=1600-(50+100) x 10 N=100N

$∴ Accelaration = \frac{100}{150} m / s^{2} = \frac{2}{3} m / s^{2}$

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