Respuesta :
Answer:
The dimension of the variable [tex]z[/tex] will be: [tex][\frac{1}{t^3}][/tex]
Step-by-step explanation:
Given equation is: [tex]v= (\frac{1}{6})zxt^2[/tex]
The dimensions of the variables [tex]v, x[/tex] and [tex]t[/tex] are [tex][\frac{l}{t}], [l][/tex] and [tex][t][/tex] respectively.
Replacing all variables by their dimensions, we will get......
[tex][\frac{l}{t}]= z[l][t]^2[/tex]
[tex]\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}][/tex]
So, the dimension of the variable [tex]z[/tex] will be: [tex][\frac{1}{t^3}][/tex]
Answer:
The dimension of z is [tex][\frac{1}{t^3}][/tex].
Step-by-step explanation:
We have been given the dimension of [tex]v=[\frac{l}{t}][/tex], [tex]x=[l][/tex] and [tex]t=[t][/tex]
We need to find the dimension of z
Here, l denotes the length and t denotes the time:
We will put the values of the dimension of the variables given to find the dimension of z. and 1/6 is dimensionless.So, neglect it.
[tex][\frac{l}{t}]=z\cdot [l]\cdot [t^2][/tex]
Now, we will simplify the above expression so, as to get the value of z
[tex][\frac{l}{t\cdot t^2\cdot l}]=z[/tex]
[tex]\Rightarrow z=[\frac{1}{t^3}][/tex]
Hence, the dimension of z is [tex][\frac{1}{t^3}][/tex]
