Question

Which one of the following is equal to 1 newton?
$
  {\text{A}}{\text{. 1kg}}{\text{.}}{{\text{m}}^2}{\text{/s}} \\
  {\text{B}}{\text{. 1kg}}{\text{.m/}}{{\text{s}}^2} \\
  {\text{C}}{\text{. 1k}}{{\text{g}}^2}{\text{/s}} \\
  {\text{D}}{\text{. 1k}}{{\text{g}}^2}{\text{.m/s}} \\
 $

Answer 1

Hint: Newton is the SI unit of force and force applied on a body is equal to the product of mass of the body and acceleration produced in the body by the applied force. By relating the units of force with that of mass and acceleration, we can get the required answer.

Formula used:
The Newton’s second law of motion is given as
$F = ma$

Complete step-by-step answer:
We are asked to find the units of force in terms of the units of mass, length and time. We know that Newton’s second law of motion relates the force applied on a body with its mass and the acceleration produced in it. It states that the force applied on a body is equal to the product of mass of the body and acceleration produced in the body by the applied force. It is given as
$F = ma$
Now we know that the SI units of these quantities are as follows:
Force: newton (N)
Mass: kilogram (kg)
Acceleration: metres per square seconds ($m/{s^2}$)
Now when we insert these units into the expression of Newton’s second law of motion, we get
$
  1N = 1kg \times 1m/{s^2} \\
   \Rightarrow 1N = 1kgm/{s^2} \\
 $
This is the required answer. Hence, the correct answer is option B.

So, the correct answer is “Option B”.

Note: It should be noted that we also have a similar relation between the units of these quantities in other systems of units. For example, in the CGS system of units, the unit of force is dyne, the unit of mass is grams while the unit of acceleration is $cm/{s^2}$. In this case, we have the following relation.
$1dyne = 1gcm/{s^2}$
The relation between one newton and one dyne is given as follows:
$1N = {10^5}dyne$