Dimensions

Classical Mechanics Level 2

If $[y]$ and $[x]$ denote the dimensions of physical quantities $x$ and $y$ respectively. Find the dimensions of $d^2y/dx^2$ .

[y]/[x]^3

[y]^2/[x]

[y]/[x]^2

[y]^2/[x]^2

[y]/[x]

[y]/[x]^0

2 solutions

Md Zuhair
Sep 1, 2016

we know that $dy/dx$ = Change in y / change in x. Then Dimensions of $dy/dx= [y]/[x]$ . And for double derivative. $d^2y/dx^2$ = $d/dx(dy/dx)$ = $[y]/[x]^2$

I have changed the wording of problem here. $[x]$ and $[y]$ are not physical quantities but dimensions of these physical quantities. As for Find the roots . Is the answer, the number of roots or the sum of roots? Anyway, I used numerical method, there is only one root $x = 0.509430499$ .

Chew-Seong Cheong - 4 years, 9 months ago

How did you did it? Please tell me.

Md Zuhair - 4 years, 9 months ago

Just plot the graph to see that there is only one root. Then use Newton Raphson method .

Chew-Seong Cheong - 4 years, 9 months ago

You can also use Wolfram Alpha see here . It is online and free.

Chew-Seong Cheong - 4 years, 9 months ago

Steven Chase
Sep 2, 2016

For example, if $y$ represents position and $x$ represents time, we know from experience that the second derivative has units of $[y]/[x]^{2}$ , which would be $m/s^{2}$ in the real world.

Hmmm.. But Proofing without examples is also a part of tough game.

Md Zuhair - 4 years, 9 months ago

Dimensions

2 solutions

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