Question

What are the s.i units of k so that the equation velocity =k × density is dimensionally correct give your answer in terms of the basic units (kg-¹m45-¹

Answer 1

Answer:

SI unit of K is :

K=m^4/s-kgK=m4/s−kg

Explanation:

The relation that is dimensionally correct is :

\text{ velocity}=\text{K}\timed \text{Density} velocity=K×Density

The SI unit of velocity is m/s and the Si unit of density is kg/m^3kg/m3 .

Putting the SI units of both quantities, we get :

m/s=K\times kg/m^3m/s=K×kg/m3

In terms of dimensions,

[LT^{-1}]=K\times [ML^{-3}][LT−1]=K×[ML−3]

Dimension of K is :

[K]=[M^{-1}L^4T^{-1}][K]=[M−1L4T−1]

SI unit of K is :

K=m^4/s-kgK=m4/s−kg

Hence, this is the required solution.