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?

The dimension of the variable will be:  

Step-by-step explanation:

Given equation is:  

The dimensions of the variables and are   and respectively.

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

So, the dimension of the variable will be:  

The dimension of z is .

Step-by-step explanation:

We have been given the dimension of  , and

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.

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

Hence, the dimension of z is

kjgfcvbjkl

step-by-step explanation:

sdfghjkl; vbnm,

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.