# Dimensional consistency problem, need help

**1. The problem statement, all variables and given/known data**

Problem is, quote:

The period of a simple pendulum, defined as the time for one complete oscillation, is measured in time units and is given by:

T = 2∏√l/g

where,l is the length of the pendulum and g is the acceleration due to gravity,* in units of length divided by time squared.* Show that this equation is dimensionally consistent; that is, show that the right hand side of this equation gives units of time.

**2. Relevant equations**

The solution is actually given. The full equation was as follows:

[2∏√l/g]= √L/L/t^{2}. This all equals: √t^{2} which = T

**3. The attempt at a solution**

Given the description which is italicized, I understood how they got: √L/L/t^{2} which ultimately equals T, but I do not understand how "2∏" disappeared so easily in the process of equating T.

My attempt: The italicized description already tells us that "g"= L/t^{2}. Given this information, dividing "L" by L/t^{2} will result in t^{2} (all under the square root symbol). Then, the √t^{2} is T. I get stuck on the conversion process when it comes to 2∏ however.

I’ve thought about it for several minutes, and I still can’t understand how to mathematically describe T and the aforementioned equation including 2∏. Can anyone help? Thank you for your time.

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

http://ift.tt/P4MxFO

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