Question

A force of $5\;N$ acts on the body of weight $9.8\;N$. What is the acceleration produced in $m/{\sec ^2}$?
A. $49.00\;m/{\operatorname{s} ^2}$
B. $5.00\;m/{\operatorname{s} ^2}$
C. $1.46m/{\operatorname{s} ^2}$
D. $0.5\;m/{\operatorname{s} ^2}$

Answer 1

The difference between mass and weight is to be probed upon. The relation between mass and weight needs to be determined and then applied to find out the mass of the body. The concept behind Newton’s second law of motion and its corresponding formula is applied in order to find the acceleration of the body.

Complete step by step answer:
The problem revolves around the principle behind Newton’s second law of motion and the concepts of mass and weights of a body. In order to find the acceleration we first need to understand these concepts. Let us first define the quantity known as force. Force is said to be a push or pull which changes or tends to change the state of rest or uniform motion or the direction of motion of a body.

This force that is applied will tend to change the motion of the body which may be measured in terms of the speed of the body. There will be a change in the speed or the motion of the body with time and hence this is where the acceleration of the object comes into picture.

The acceleration produced is due to the external force that is applied on the body. This is what is given as the principle of Newton’s second law. Newton's second law of motion states that the acceleration of a body is produced due to the net force that is applied on it and is inversely related to the mass of the body. Hence, the equation for Newton’s second law is given as:
$F = ma$
By rearranging the terms we get the equation for acceleration:
$a = \dfrac{F}{m}$ --------($1$)

Let us now extract the data given in the question. We are given the force that is applied on a body. However, we are given the weight of the body instead of the mass of the body. The mass of the body is not equal to the weight of the body; they are two differing quantities.
The mass is said to be the amount of matter contained in the body while the weight is said to be the amount of force that is applied on the body due to the effect of gravity and hence this is measured in Newton. The mass of a body is independent of gravity unlike weight.

Given, $F = 5\;N$ and $w = 9.8\;N$.Let us now determine the relationship between the mass and weight of a body in order to convert the weight in terms of mass. This is done because the acceleration is dependent upon the mass of the body and not on its weight. This is given by the relation:
We know that,
$Weight = mg$
Hence,
$m = \dfrac{{Weight}}{g}$
The variable $g$ indicates the acceleration due to gravity which has a constant value which is given as $9.8\,m/{\operatorname{s} ^2}$.

By substituting the given values we get:
$m = \dfrac{{9.8}}{{9.8}}$
$\Rightarrow m = 1\;kg$
Hence this mass that is obtained is substituted in equation ($1$) to get the value of acceleration:
$a = \dfrac{5}{1}$
Since the SI unit of acceleration is $m/{s^2}$ we get:
$a = 5\;m/{s^2}$
We round this off to three significant figures to get:
$\therefore a = 5.00\;m/{s^2}$
Hence, the acceleration of the body in $m/{\sec ^2}$ is given as $5.00\;m/{\operatorname{s} ^2}$.

Therefore, the correct answer is option B.

Note: The quantities of mass and weight seem similar in concepts but they are in reality not the same or equal in value. This is a common error that can be made in these types of problems where the weight of the body is substituted instead of the mass value. The conversion is not done which is incorrect. The body which is said to be lighter, that is, it is a body which has a smaller mass then the acceleration on it will be more and vice-versa.