Mathematics: 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?

Consider the equation v = (1/6)zxt2. the dimensions

joseroblesrivera123

10.03.2022

The dimension of the variable will be: $[\frac{1}{t^3}]$

Step-by-step explanation:

Given equation is: $v= (\frac{1}{6})zxt^2$

The dimensions of the variables v, x and are $[\frac{l}{t}], [l]$ and [t] respectively.

Replacing all variables by their dimensions, we will get......

$[\frac{l}{t}]= z[l][t]^2$

$\frac{[l]}{[t]}= z[l][t^2]\\ \\ z= \frac{[l]}{[t][l][t^2]}=\frac{1}{[t][t^2]}=\frac{1}{[t^3]}=[\frac{1}{t^3}]$

So, the dimension of the variable will be: $[\frac{1}{t^3}]$

0,0(0 оценок)

ashah1260

10.03.2022

The dimension of z is $[\frac{1}{t^3}]$ .

Step-by-step explanation:

We have been given the dimension of $v=[\frac{l}{t}]$ , x=[l] and t=[t]

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.

$[\frac{l}{t}]=z\cdot [l]\cdot [t^2]$

Now, we will simplify the above expression so, as to get the value of z

$[\frac{l}{t\cdot t^2\cdot l}]=z$

$\Rightarrow z=[\frac{1}{t^3}]$

Hence, the dimension of z is $[\frac{1}{t^3}]$

0,0(0 оценок)

rockstargirl9869

15.03.2020

85/100

Step-by-step explanation:

just take all the uneeded numbers out and it is 85/100

0,0(0 оценок)