Rocket Propulsion MCQ - Practice Questions with Answers

Before firing the rocket from launching pad its initial momentum is zero.

But when the rocket is fired from the launch pad, to conserve momentum the exhaust gas rush downwards at a high speed and that's how rocket moves upwards.

1. Thrust on the rocket

$$F=-\frac{udm}{dt}-mg$$

Where F= Thrust
$\frac{dm}{dt}=$ rate of ejection of the fuel

u=velocity of exhaust gas

m=mass of the rocket at any instant

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

2. Acceleration of Rocket (a)

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

• If g is neglected then

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

3. Instantaneous Velocity of Rocket (v)

$$v=u{\log }_e\left(\frac{m_{\circ }}{m}\right)-gt$$
$$\begin{array}{c}\text{ - If }\mathrm{g}\text{ is neglected then }\\ v=u\ast {\log }_e\left(\frac{m_{\circ }}{m}\right)=2.303u\ast {\log }_{10}\left(\frac{m_{\circ }}{m}\right)\end{array}$$

Where $m_0=$ initial mass of the rocket

4. 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

$$V_b=V_{max}=u{\log }_e\left(\frac{m_{\circ }}{m_r}\right)$$

$V_b\to$ burnt speed
$m_r\to$ residual mass of empty container