Question

Given unit $kg.m/{{s}^{2}}$ is the unit of:
A. Momentum
B. Velocity
C. Force
D. Acceleration

Answer 1

Hint: We will need to define all the given physical quantities in the options. Using their basic expressions we will find the units for those. Then we will compare the units we found with the unit given in the question and then we will select the right choice.

Complete step by step answer:
We will start with the first option, momentum. Momentum is defined as the product of mass and velocity of a body. It is a vector quantity. So the expression for momentum will be,
$p=m\times v$
Where $m$ is mass and $v$ is the velocity. So the unit of momentum will be,
\[p=kg\times \dfrac{m}{s}=kg.m/s\]
The unit of momentum is found to be \[kg.m/s\].
Now, if we look at the second option, velocity. Velocity is defined as the rate of change of displacement of a body. The expression for velocity is,
\[v=\dfrac{x}{t}\]
Here, \[x\]is the displacement and \[t\] is the time. So, the unit of velocity will be,
\[v=\dfrac{m}{s}=m/s\]
The unit of velocity is found to be \[m/s\].
If we take the third option, force. Force is given by the product of mass and acceleration of a body.
That is, $F=m\times a$. Where acceleration $a$ is the rate of change of velocity. So, the unit of force will be,
$F=kg\times \dfrac{m}{{{s}^{2}}}=kg.m/{{s}^{2}}$
Therefore the unit of force is found to be $kg.m/{{s}^{2}}$.
Now, the last option acceleration which is given as rate of change of velocity has its unit as \[m/{{s}^{2}}\].
So, if we compare these units with the given unit in the question, we can find that force is having the unit $kg.m/{{s}^{2}}$. Hence, option c is the correct answer.

Note:
We can easily solve these types of questions by remembering the units of basic physical quantities. We can just look at the question and assume that $kg$ is the unit of mass and $m/{{s}^{2}}$ is the unit of acceleration. So the answer will be the physical quantity which is defined as the product of mass and acceleration. We can also find the units in different quantities from its dimensional formulas.