Mathematics, 26.06.2019 14:30 diontna29
Consider the equation v = (1/6)zxt2. the dimensions of the variables v, x, and t are [l/t], [l], and [t] respectively. the numerical factor 6 is dimensionless. what must be the dimensions of the variable z, such that both sides of the equation have the same dimensions?
Answers: 2
will be: ![[\frac{1}{t^3}]](/tpl/images/0019/8195/8131b.png)
and 
are ![[\frac{l}{t}], [l]](/tpl/images/0019/8195/4de48.png)
and ![[t]](/tpl/images/0019/8195/ada43.png)
respectively. ![[\frac{l}{t}]= z[l][t]^2](/tpl/images/0019/8195/a4378.png)
![\frac{[l]}{[t]}= z[l][t^2]\\ \\ z= \frac{[l]}{[t][l][t^2]}=\frac{1}{[t][t^2]}=\frac{1}{[t^3]}=[\frac{1}{t^3}]](/tpl/images/0019/8195/faf78.png)
![v=[\frac{l}{t}]](/tpl/images/0019/8195/f9f57.png)
, ![x=[l]](/tpl/images/0019/8195/e5228.png)
and ![t=[t]](/tpl/images/0019/8195/a3263.png)
![[\frac{l}{t}]=z\cdot [l]\cdot [t^2]](/tpl/images/0019/8195/6b752.png)
![[\frac{l}{t\cdot t^2\cdot l}]=z](/tpl/images/0019/8195/3b1e2.png)
![\Rightarrow z=[\frac{1}{t^3}]](/tpl/images/0019/8195/e99a9.png)
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Consider the equation v = (1/6)zxt2. the dimensions of the variables v, x, and t are [l/t], [l], and...
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