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T is in seconds (s) 

2pi is dimensionless 

L is in meters (m) 

g is in meters per second squared (m/s^2) 

so you can write the equation for the period of the simple pendulum in its units... 

s=sqrt(m/(m/s^2)) 

simplify

s=sqrt(m*s^2*1/m) cancelling the m's 

s=sqrt(s^2) 

s=s 

therefore the dimensions on the left side of the equation are equal to the dimensions on the right side of the equation.

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