Question

derive the dimensional formula for density​

Answer 1

Answer:

Dimensions of common physical quantities

Quantity Relation Dimension

stress force/area [MT−2L−1]

pressure force/area MT−2L−1]

density mass/volume [ML−3]

strain displacement/length [1]

Answer 2

Answer:

As we know that the density is defined as the mass per unit volume.

Formula of density -

$\\ \large{ \boxed{ \sf{Density = \frac{mass}{volume} }}} \qquad \quad \: \: \: \: \sf(i)$

Dimensional formula of mass -

$\\ \sf ({M}^{1} {L}^{0} {T}^{0} ) \qquad \quad \quad \qquad \: (ii)$

Where,

• M = Mass
• L = Length
• T = Time.

Dimensional formula of volume -

$\\ \sf( {M}^{0} \: {L}^{3} \: {T}^{0} ) \qquad \qquad \quad \qquad \: (iii)$

Now, by substituting equation 2 and 3 in equation 1 -

$\\ \sf \: {M}^{0} \: {L}^{3} \: {T}^{0} \: \times \: {M}^{1} \: {L}^{0} \: {L}^{0} \\ \\ \\ \star \: \large{ \boxed{ \sf \bigg ( \: {M}^{1} \: {L}^{ - 3} \: {T}^{0} \: \bigg)}}$