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Rocket Propulsion - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Rocket Propulsion is considered one of the most asked concept.

  • 5 Questions around this concept.

Concepts Covered - 1

Rocket Propulsion

Let us assume a rocket of total initial mass (rocket + fuel) m0, starts moving upward due to thrust force of fuel jet. Assuming the velocity of fuel jet with respect to the rocket to be u (assumed to be constant for this discussion) in vertically downward direction and mass of jet fuel emerging out of rocket per unit time to be \frac{dm}{dt}. Let the velocity of rocket after t time of motion be v and the acceleration of the rocket be a in vertically upward direction.

  1. Thrust on the rocket

F=-\frac{udm}{dt}

Where F= Thrust

\frac{dm}{dt}= rate\:of\;ejection\:of\:the\:fuel

u=velocity of exhaust gas with respect to rocket

m=mass of the rocket at time t

Net force on rocket-

F_{net}=-\frac{udm}{dt}-mg

  • \ast \:F=-\frac{udm}{dt}\:[\:if\:gravity\:neglected]

  1. Acceleration of Rocket (a)

          a=-\frac{u}{m}\:\frac{dm}{dt}-g

  • If g is neglected then

               a=-\frac{u}{m}\:\frac{dm}{dt}

  1. Instantaneous Velocity of Rocket (v)

 If g is neglected then-

\\ a=-\frac{u}{m}\:\frac{dm}{dt}\\ \\ \frac{dv}{dt}=-\frac{u}{m}\:\frac{dm}{dt}\\ \\ \int_{0}^{v}dv=-u\int_{m_{0}}^{m}\frac{1}{m}dm                       

\\ \Rightarrow v=u\:log_{e}\left ( \frac{m_{\circ }}{m} \right )

 v=u*log_{e} ( \frac{m_{\circ }}{m})=2.303u*log_{10} ( \frac{m_{\circ }}{m})

  1. Burnt speed of Rocket

  • It is the speed attained by the rocket when complete fuel gets burnt.

  • It is the maximum speed attained by the rocket

  • Formula

 V_{b}=V_{max}=u\:log_e\left ( \frac{m_\circ }{m_r} \right )

V_{b}\rightarrow burnt \:speed

m_{r}\rightarrow residual\:mass\:of\:empty\:container

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Rocket Propulsion

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