Question

A rocket of mass$100kg$ burns $0.1kg$ of fuel per second. If the velocity of exhaust gas is $1km{s}^{-1}$, then it lifts with an acceleration of

• A. $1000m{s}^{-2}$
• B. $100m{s}^{-2}$
• C. $10m{s}^{-2}$
• D. $1m{s}^{-2}$

Answer 1

The correct option is D

$1m{s}^{-2}$

Step 1. Given Data,

Let $F$ is the force on the rocket.

Velocity $V=1000m{s}^{-1}$

$=1km{s}^{-1}$

Mass $m=100Kg$

Burned fuel per second $\frac{dm}{dt}=0.1Kg/s$

Step 2. We have to calculate the acceleration which lifts the rocket,

We know that,

Thrust force,

$$\begin{gathered} F=V\times \left(\frac{dm}{dt}\right) \\ \Rightarrow F=1000x0.1 \\ \Rightarrow F=100N \end{gathered}$$

Now,

$$\begin{gathered} F=ma \\ \Rightarrow a=\frac{F}{M}m{s}^{-2} \\ \Rightarrow a=\frac{100}{100}m{s}^{-2} \\ \Rightarrow a=1m{s}^{-2} \end{gathered}$$

Then, the acceleration which lifts the rocket is $1m{s}^{-2}$.

Hence, the correct option is $\text{'}D\text{'}$.