Question

In a rocket, fuel burns at the rate of $2kg/s$. This fuel gets ejected from the rocket with a velocity of \[80km/s\]. Force exerted on the rocket is
$\begin{align}
  & A)16000N \\
 & B)160000N \\
 & C)1600N \\
 & D)16N \\
\end{align}$

Answer 1

Hint: From Newton’s second law of motion, we know that force exerted on an object is equal to the product of mass of the object and the acceleration of the object. In the case of ejection of fuel from a rocket, force exerted can also be defined as the product of rate of change of mass with respect to time and the velocity of the ejected fuel.

Formula used:
$\begin{align}
  & 1)F=ma \\
 & 2)F=\dfrac{dm}{dt}v \\
\end{align}$

Complete step by step answer:
From Newton’s second law of motion, we know that force exerted on an object is equal to the product of mass of the object and the acceleration of the object. This is mathematically expressed as:
$F=ma$
where
$F$ is the force exerted on an object
$m$ is the mass of the object
$a$ is the acceleration of the object
Let this be equation 1.
In the case of ejection of fuel from a rocket, force exerted can also be defined as the product of rate of change of mass of the fuel with respect to time and the velocity of the ejected fuel. This can be be mathematically expressed as:
$F=\dfrac{dm}{dt}v$
where
$F$ is the force exerted on a rocket due to ejection of fuel
$\dfrac{dm}{dt}$ is the rate of change of mass of fuel with respect to time
$v$ is the velocity of the ejected fuel
Let this be equation 2.
Coming to our question, we are given that
$\dfrac{dm}{dt}=2kg/s$
\[v=80\times {{10}^{3}}m/s\]
Substituting these values in equation 2, we have$F=\dfrac{dm}{dt}v=2kg{{s}^{-1}}\times 80\times {{10}^{3}}m{{s}^{-1}}=160000kgm{{s}^{-2}}=160000N$

So, the correct answer is “Option B”.

Note: The solution needs to be deduced from Newton’s second law, as already mentioned. Newtons’ second law of motion can be rearranged in different ways as given below:
$F=ma=\dfrac{dm}{dt}v=m\dfrac{dv}{dt}$
The correctness of the above expression can be deduced from their units, as given below:
\[N=kgm{{s}^{-2}}=(kg{{s}^{-1}})(m{{s}^{-1}})=kg(m{{s}^{-2}})\]