Q. The rate of mass of the gas emitted from rear of a rocket is initially $0.1\ kg/sec$. If the speed of the gas relative to the rocket is $50\ m/sec$ and mass of the rocket is $2\ kg$, then the acceleration of the rocket in $m/s{ec}^{2}$ is
A) 5
B) 5.2
C) 2.5
D) 25
Explanation
(c) $\frac{dM}{dt} = 0.1kg/s,\ v_{gas} = 50\ m/s$,
Mass of the rocket = $2\ kg.$ $Mv =$ constant
$- v\frac{dM}{dt} + M\frac{dv}{dt} = 0$ $\therefore\frac{dv}{dt} = \frac{1}{M}v\frac{dM}{dt}$
$\Rightarrow \ $Acceleration$\ = \frac{1}{2} \times 50 \times 0.1 = 2.5\ m/s^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.