Question

A rocket with a lift-off mass $3.5\times {{10}^{4}}Kg$ is blasted upwards with an initial acceleration of $10m{{s}^{-2}}$. The initial thrust of the blast is:
$\begin{align}
  & \text{A}\text{. }3.5\times {{10}^{5}}N \\
 & \text{B}\text{. }7\times {{10}^{5}}N \\
 & \text{C}\text{. }1.40\times {{10}^{5}}N \\
 & \text{D}\text{. }1.75\times {{10}^{5}}N \\
\end{align}$

Answer 1

Hint: Thrust is described as the force which moves the rocket through the air, and through the space. Thrust is generated with the help of the propulsion system of the rocket through the application of the third law of Newton which says that for every action there is an equal and opposite reaction. We will calculate the value of initial thrust of the blast by finding the net force acting on the rocket during its lift-off.

Formula used:
Thrust on the rocket, $T=m\left( g+a \right)$

Complete step-by-step answer:
Like all other objects in nature, working of a rocket is also governed by Newton's Laws of Motion.
The First Law of Newton describes how an object acts when no force is acting upon it. So, the rocket stays still until a force is applied to move it. Likewise, once it’s in motion, it won't stop until a force is applied on it.
Newton's Second Law explains that the more mass an object possesses, the more force is required to move it. A larger rocket will need stronger forces, for example more fuel, to make it accelerate.
Newton's Third Law states that every action carries an equal and opposite reaction. In a rocket, the burning fuel creates a push, exerts force, on the front of the rocket and pushes it in the forward direction. This creates an equal and opposite push, or force, on the exhaust gas backwards.

The downward force acting on the rocket is the force due to gravity, that is $mg$
The downward force acting on the rocket is the thrust, that is $T$
Net force acting on the rocket is,
$F=T-mg$
The net force acts in the upward direction.
The acceleration due to gravity is,
$g=10m{{s}^{-2}}$
Now,
$\begin{align}
  & T-mg=ma \\
 & T=m\left( g+a \right) \\
\end{align}$
Given that lift-off mass of the rocket is $3.5\times {{10}^{4}}Kg$
Also,
The acceleration of the rocket is $10m{{s}^{-{{2}^{{}}}}}$
Put,
$\begin{align}
  & m=3.5\times {{10}^{4}}Kg \\
 & g=10m{{s}^{-2}} \\
 & a=10m{{s}^{-2}} \\
\end{align}$
$\begin{align}
  & T=m\left( g+a \right)=3.5\times {{10}^{4}}\left( 10+10 \right) \\
 & T=3.5\times {{10}^{4}}\times 20=7\times {{10}^{5}}N \\
\end{align}$
The initial thrust of the blast is $7\times {{10}^{5}}N$

So, the correct answer is “Option B”.

Note: A rocket can lift off from a launch pad only when it expels the gases out of its engine. The rocket pushes on the propulsion gas, and the gas in turn pushes on the rocket. The rocket has to produce a lot of thrust to escape the earth's gravitational pull. In a rocket, the action is the expelling of gas out of the engine and the reaction is the movement of the rocket in the opposite direction.