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^1 m45^-1)

Answer 1

Answer: M is mass, L is length and T is time in SI Unit

Kindly see the picture I have solved it as required

Answer 2

SI unit of K is :

$K=m^4/s-kg$

Explanation:

The relation that is dimensionally correct is :

$\text{ velocity}=\text{K}\times \text{Density}$

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

Putting the SI units of both quantities, we get :

$m/s=K\times kg/m^3$

In terms of dimensions,

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

Dimension of K is :

$[K]=[M^{-1}L^4T^{-1}]$

SI unit of K is :

$K=m^4/s-kg$

Hence, this is the required solution.

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