So the correct SI units for the quantity A are meters (m).

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Discussion Overview

The discussion revolves around determining the correct SI units for the quantity A, defined by the equation A=√(R/TY), where R, T, and Y have specified SI units. Participants explore the implications of different interpretations of the equation and the resulting unit simplifications.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the equation A=√(R/TY) and specifies the SI units for R, T, and Y.
  • Another participant questions the notation and asks for clarification on whether the expression is interpreted as √(R/(TY)) or (√R)/TY.
  • A third participant confirms the first interpretation, indicating that the entire expression R/TY is under the square root.
  • Subsequent posts provide a step-by-step simplification of the units, leading to the conclusion that the units of A are meters.
  • One participant attempts to clarify the simplification process, showing how the units cancel out to yield meters.

Areas of Agreement / Disagreement

While there is a consensus on the final result being meters, there is some ambiguity regarding the notation and interpretation of the equation, which has led to different initial understandings among participants.

Contextual Notes

The discussion includes varying interpretations of the equation's notation, which may affect the understanding of the unit derivation. The assumptions regarding the expressions and their simplifications are not fully resolved.

tommyboo
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I am having a problem finding the correct SI unitsfor the quantity A?

In the equation

A=√(R/TY)

That is A equals the square root of R divided by TY

(not to good showing workings on the computer sorry)

, the SI units of the quantity R are kg m^3 s^–2, the SI units of the quantity T are kg and the SI units of the quantity Y are m s^–2. What are the correct SI units for the quantity A?
 
Last edited:
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tommyboo said:
I am having a problem finding the correct SI unitsfor the quantity A?

In the equation

A=√R/TY

That is A equals the square root of R divided by TY
Both your notation and explanation are ambiguous.

Is the expression on the right side this?
\sqrt{\frac{R}{TY}}
or this?
\frac{\sqrt{R}}{TY}
tommyboo said:
(not to good showing workings on the computer sorry)

, the SI units of the quantity R are kg m^3 s^–2, the SI units of the quantity T are kg and the SI units of the quantity Y are m s^–2. What are the correct SI units for the quantity A?
 
The first one R/ty all square root. Do apologise for the bad format
 
Then, the units of A are meters.
 
To clarify gsal's answer...

You have the expression
\sqrt{\frac{R}{TY}}

Simply, insert the units for each variable (in place of the variables):
\sqrt{\frac{\frac{kg\cdot m^3}{s^2}}{(kg)(\frac{m}{s^2})}}

and simplify...
\sqrt{\left(\frac{kg \cdot m^3}{s^2}\right) \left(\frac{s^2}{kg \cdot m}\right)}

kg and s2 cancel out, leaving
\sqrt{\frac{m^3}{m}}

which is
\sqrt{m^2}

or, more simply m
 

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