Question

In the case of rocket propulsion, choose the correct option(s).

• A. Momentum of system (rocket + fuel) always remains constant.
• B. Newton's third law is applied.
• C. If exhaust velocity and rate of burning of mass is kept constant, then acceleration of the rocket will go on increasing.
• D. Newton's second law can be applied.

Answer 1

Answer: (B), (C), (D)

Newton's second law can be applied.

On the system (rocket + fuel), external force of gravity acts, therefore its momentum does not remain constant.

When exhaust leaves the rocket, it applies an upthrust on the rocket which helps the rocket to go up. Rocket in turn applies force on the exhaust pushing it down. Hence, Newton's third law is applied.

We can use Newton's second law of motion as we are analysing the motion of rocket from inertial frame of reference i.e earth. Newton's second law is applicable in inertial frame of reference.
i.e $F_{net}=F_t-w=v_r\left(\frac{-dm}{dt}\right)-mg$
[where, $v_r\to$ Exhaust velocity
$\frac{-dm}{dt}\to$ Rate of burning of mass
$w\to$weight of rocket $=mg$ (downward)
$F_t\to$Thrust force (upward) ]

$\therefore$ Net force on rocket,
$ma=v_r\left(\frac{-dm}{dt}\right)-mg$
$a=\frac{v_r}{m}\left(\frac{-dm}{dt}\right)-g$
$\Rightarrow a\propto \frac{1}{m}$
[ $\because v_r$ and $\frac{-dm}{dt}$ are constant.]
Thus, accelartion $a$ goes on increasing as mass $m$ goes on decreasing at the constant rate of $\frac{dm}{dt}$.
Options B, C and D are correct.