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VITEEE 2017 Paper

Section: Physics

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Question : 1 of 125

Marks: +1, -0

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20 m/

s^2

, the amount of gas ejected per second to supply the needed thrust will be (Take g = 10 m/

s^2

)

127.5 kg/s
137.5 kg/s
155.5 kg/s
187.5 kg/s

Solution:

Given that, Mass of rocket

m=5000\;\mathrm{Kg}

Acceleration

a=20\;\mathrm{m}/\mathrm{s}^{2}

Speed

v=800\;\mathrm{m}/\mathrm{s}

g=10\;\mathrm{m}/\mathrm{s}^{2}

Now, thrust force on the rocket

F_{t}=v_{r}\left(-\frac{dm}{dt}\right)

Net force on the rocket

F_{\text{net}}=F_{t}-W

ma=v_{r}\left(-\frac{dm}{dt}\right)-mg

\left(-\frac{dm}{dt}\right)=\frac{m(g+a)}{v_{r}}

Rate of gas ejected per second

\left(-\frac{dm}{dt}\right)=\frac{5000(10+20)}{800}

-\frac{dm}{dt}=187.5\;\mathrm{kg}/\mathrm{s}

Hence, the amount of gas ejected per second is

187.5\;\mathrm{kg}/\mathrm{s}

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