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Since dimension doesn't depend on magnitude. Hence, if a relation is dimensionally correct then it doesn't mean that it will also be mathematically or physically correct.

What will be the vice-versa?

Please answer these three questions.

Q1. If a relation is dimensionally incorrect, can it be mathematically correct?

Q2. If a relation is mathematically correct, can it be dimensionally incorrect?

Q3. If a relation is mathematically incorrect, can it be dimensionally correct?

https://youtu.be/AbB_j4uPNrM?t=65 <--- check out the video for reference, watch it till the 4th minute and listen to the last statement carefully.

Chrishiv Tamta
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  • Welcome to MSE. Please explain what have you tried. Where are you stuck? Questions showing no effort tend to be voted down and/or closed. – Andrei Sep 10 '20 at 05:02
  • Please follow the link for reference. [link] https://www.toppr.com/ask/question/mention-any-two-limitations-of-dimensional-analysis/ [link] – Chrishiv Tamta Sep 11 '20 at 00:42
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    Here is an example: area of a disk is $A=\pi R^2$. You measure area in $m^2$ and radius in $m$. Try each of the questions. What conclusions do you get? – Andrei Sep 11 '20 at 00:59
  • [link] https://youtu.be/AbB_j4uPNrM?t=65 [link] hello andrei, thank you for your response. please check out the video you'll surely get what i'm trynna say. watch the video till the 4th minute. – Chrishiv Tamta Sep 11 '20 at 01:09
  • He misspoke in the video. If the expression is mathematically correct, it is dimensionally correct as well – Andrei Sep 11 '20 at 02:32
  • thank you so much andrei for your time. – Chrishiv Tamta Sep 11 '20 at 09:42

1 Answers1

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Dimensional analysis is a heuristic you can use to check whether a relation is "obviously wrong". Checking that the dimensions are correct is like checking whether your answer is positive when you expect a positive answer. You can probably answer your own questions by replacing "is dimensionally correct" with "has the correct sign".

Q1: If a relation has the wrong sign, can it be mathematically correct?

Q2: (This is actually the same as Q1).

Q3: If a relation is mathematically incorrect, can it still have the same sign?

1Rock
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  • [link] youtu.be/AbB_j4uPNrM?t=65 [link] hello 1rock, thanks for the response. please check out the video you'll surely get what i'm trynna say. watch the video till the 4th minute. – Chrishiv Tamta Sep 11 '20 at 01:15
  • I can't watch videos at the moment, can you explain what it says? – 1Rock Sep 11 '20 at 01:18
  • i can't understand this statement. the lecturer is saying "dimensions don't depend on the magnitude. so, if a given relation is dimensionally correct then it doesn't mean that the relation will also be mathematically correct. its vice-verse is if a relation is mathematically incorrect on the base of some law of physics, it has to be dimesionally correct." – Chrishiv Tamta Sep 11 '20 at 01:24
  • But obviously that's wrong. If a relation is mathematically incorrect, it obviously doesn't have to be dimensionally correct. – 1Rock Sep 11 '20 at 01:26
  • that's the same what i was thinking. still, please check out the video whenever it will be feasible for you. thank you so much for your help :) – Chrishiv Tamta Sep 11 '20 at 01:30