Question

A rocket is going upwards with accelerated motion. A man sitting in it feels his weight increased $5$ times his own weight. If the mass of the rocket including that of the man is $1.0\times {{10}^{4}}\text{ kg}$, how much force is being applied by the rocket engine?
A.$5\times {{10}^{4}}\text{ N}$
B.$5\times {{10}^{5}}\text{ N}$
C.$5\times {{10}^{8}}\text{ N}$
D.$2\times {{10}^{4}}\text{ N}$

Answer 1

Hint: To solve this problem we will have to use the concept of acceleration due to gravity. If the man sitting in the rocket feels his weight increased $5$ times his own weight then he must have experienced $5$ times the acceleration due to gravity. After knowing this we can easily find out the force applied by the rocket engine.

Complete answer:
If the man sitting in the rocket feels his weight increased $5$ times his own weight then the acceleration due to gravity acting on the man as well as the rocket must be:
$a=5g$
The acceleration due to gravity is the acceleration that a body gains due to the gravitational force of the Earth that is directed towards the center of the Earth. The acceleration due to gravity can be taken as $g=10\text{ m}\cdot {{\text{s}}^{-2}}$, therefore the value of acceleration acting on the system (rocket and the man) would be as follows:
$\begin{align}
  & a=5\times 10 \\
 & \Rightarrow a=50\text{ m}\cdot {{\text{s}}^{-2}} \\
\end{align}$
It is given that the mass of the rocket including that of the man is $1.0\times {{10}^{4}}\text{ kg}$, therefore the force applied by the rocket engine will be as follows:
$\begin{align}
  & F=ma \\
 & \Rightarrow F=1.0\times {{10}^{4}}\times 50 \\
 & \therefore F=5\times {{10}^{5}}\text{ N} \\
\end{align}$

Thus, the correct option is $B$.

Note:
The rocket has to apply a force that will support the increased weight that will exert a gravitational force directed towards the center of the Earth. The gravitational force is the product of the mass of the body and the acceleration due to gravity acting on the body at that particular point and will change if any of these two quantities increases or decreases.