Question

If force (F), length (L) and time (T) be considered fundamental units, then units of mass will be
A.)$\left[ FL{{T}^{-2}} \right]$
B.)$\left[ F{{L}^{-2}}{{T}^{-1}} \right]$
C.)$\left[ F{{L}^{-1}}{{T}^{2}} \right]$
D.)$\left[ {{F}^{2}}L{{T}^{-2}} \right]$

Answer 1

Hint: In simple words, force is the product of mass and acceleration. Acceleration is nothing but velocity per unit square of time. Whereas velocity is displacement per unit time. S.I unit of force is the Newton. S.I unit of mass is kg. S.I unit of length is meter. S.I. unit of time is second. Question is about dimension and not for the unit. Notice that in option dimension of force is not N but F. so don’t write N instead write F.

Complete step by step solution:
When we kick the ball, the ball moves. If we don’t kick it then it will remain in steady-state. So unless and until we act a force of the ball, the ball will not move. Force on the ball will be by kick or air.

So now we know that force is nothing but acceleration on mass. Therefore force is defined as
We know that force is given by,

Force = mass × acceleration

Mathematically

$F=m\times a$
S.I unit of force is the Newton. Denoted by N.
S.I unit of mass is kilogram denoted by kg.
S.I unit of acceleration is meter per second Square denoted by $m/{{s}^{2}}$.

Now we know that acceleration is velocity per unit time and velocity is nothing but displacement per unit time.

So mathematically acceleration is given by

$a=m/{{s}^{2}}$

So force F in dimension is written as,

$\begin{align}
  & \left[ F \right]=\left[ ML{{T}^{-2}} \right] \\
 & \left[ F \right]=[M][L][{{T}^{-2}}] \\
 & \operatorname{Re}arrange,widget \\
 & [M]=\dfrac{[F]}{[L][{{T}^{-2}}]} \\
 & [M]=[F][{{L}^{-1}}][{{T}^{2}}] \\
 & [M]=[F{{L}^{-1}}{{T}^{2}}] \\
\end{align}$

So the answer is $[M]=[F{{L}^{-1}}{{T}^{2}}]$.
Answer- (C)

Note: Note that options given are in dimensional form. Even though they mention units of mass, options are in dimensional form. So always look for options. In most of the cases, options give you a more clear idea about the solution and aim asked in questions.