Answer:
The SI unit of R should be (m²/kg) × s.
Step-by-step explanation:
To make the equation velocity = R × density dimensionally correct, we need to ensure that the units on both sides of the equation match.
The equation is:
velocity = R × density
The SI unit of velocity is meters per second (m/s), and the SI unit of density is kilograms per cubic meter (kg/m³).
Let's analyze the dimensions on both sides of the equation:
Dimensions of velocity: [L] / [T] (Length / Time)
Dimensions of density: [M] / [L]^3 (Mass / Length cubed)
To make the equation dimensionally correct, the dimensions on both sides should be the same. So, we need to find the appropriate unit for the constant R that makes this happen.
Let's analyze the dimensions of R × density:
Dimensions of R × density: [R] × [M] / [L]^3
For the equation to be dimensionally correct, the dimensions on both sides should be equal:
[L] / [T] = [R] × [M] / [L]^3
Solving for the dimension of R:
[R] = [L]^2 / [T] × [M]
To match the dimensions, the SI unit of R should be (m²/kg) × s.
Therefore, to make the equation velocity = R × density dimensionally correct, the SI unit of R should be (m²/kg) × s.