Q. A rocket of mass $100\ kg$ burns $0.1\ kg$ of fuel per sec. If velocity of exhaust gas is $1\ km/sec$, then it lifts with an acceleration of
A) $1000\ ms^{- 2}$
B) $100\ ms^{- 2}$
C) $10\ ms^{- 2}$
D) $1\ ms^{- 2}$
Explanation
(d) $\frac{dm}{dt} = 0.1\ kg\ /\ \sec$; Mass of the rocket $= \ 100\ kg$
$v = 1\ km/\sec = 1000\ m/\sec$
$F = \frac{d(mv)}{dt} = m\frac{dv}{dt} - v\frac{dm}{dt} = 0$ as the mass is decreasing
$100a - 1000 \times 0.1 = 0$
$a = + 1\ m/s^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.