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Find the s.i unit of R so that the equation velocity = R×density is dimensionally correct. R is a constant

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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.

User Ajameswolf
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