Question

taking force, length and time as fundamental quantities. find the dimensional formula for density.

Answer 1

Density is Mass/Volume.

So we can express mass=Force/acceleration=Force×time^2/displacement.

So density will be,
$density = \frac{force \times time \times time}{displcement \times length \times length \times length}$
So the dimension will be [F^1T^2L^-4]

thanks.
Tripathy

Answer 2

"Dimensional formula refers to the representation of a complex quantity in terms of the fundamental quantities.

We know that,

$Density=\frac { { Mass } }{ { Volume } }$

$Volume\quad =\quad { length }\quad \times \quad { breadth\quad}\times \quad height$

According to Newton’s second law,

We know that

Force =$Mass\times Acceleration$

M a s s$=\frac{\text {Force}}{\text {Acceleration}}$

Acceleration $=\frac{\Delta V}{\Delta t}$

Density $=\frac{\text { Force }}{\text { Volume } \times \text { Acceleration }}$

Density $=\frac{\text { Force } \times \Delta t}{\text {Volume} \times \Delta V}$

Density $=\frac{\text { Force } \times \Delta t}{\text {Length} \times \text {Breadth} \times \text { Height } \times \Delta V}$

On substituting, the units on the formula, we get,

Density$=\frac{k g \times m \times s}{s^{2} \times m^{3} \times m}$

Thus, the dimensional formula of density is$\left[M L^{-3}\right]$"