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3. Verify if these are correct equations checking the units (dimensional analysis) F = mv? / x v2 = a x + 2 x t2 a = x v/t

3. Verify if these are correct equations checking the units (dimensional analysis) F = mv? / x v2 = a x + 2 x t2 a = x v/t

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### Dimensional Analysis of Equations This exercise involves verifying if the given equations are dimensionally consistent by checking their units through dimensional analysis. Below are the equations you need to analyze: 1. **\( F = \frac{mv^2}{x} \)** 2. **\( v^2 = ax + 2xt^2 \)** 3. **\( a = \frac{xv}{t} \)** For each equation, identify the dimensions and ensure both sides of the equation have the same dimensions. This will help verify if the equations could be correct in a physical sense.
Transcribed Image Text:### Dimensional Analysis of Equations This exercise involves verifying if the given equations are dimensionally consistent by checking their units through dimensional analysis. Below are the equations you need to analyze: 1. **\( F = \frac{mv^2}{x} \)** 2. **\( v^2 = ax + 2xt^2 \)** 3. **\( a = \frac{xv}{t} \)** For each equation, identify the dimensions and ensure both sides of the equation have the same dimensions. This will help verify if the equations could be correct in a physical sense.
Expert Solution
Step 1

3. a

F=mv2x

F=force,

Unit of force is Newton

1N=kgm/s2

dimension of force =[MLT-2]

m=mass(kg) ,dimension=[M]

v=velocity(m/s), dimension=[LT-1]

x=distance(m),dimension=[L]

F=mv2x[MLT-2]=[M][LT-1]2[L][MLT-2]=[ML2T-2][L][MLT-2]=[MLT-2]

Dimension on both sides is equal.

So, the equation is correct.

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