dimensionally consistent.

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The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in

T=2[pie][Squareroot] 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. 

Sep 2nd, 2015

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t = 2* pie * sqrt (l/g)  

t is in seconds.

pie is a number without any unit

l is in feet or meters.

g is in feet/sec^2 or meter/sec^2

l/g is in feet/(feet/sec^2) or in meter/(meter/sec^2)

so l/g is in sec^2

sqrt(l/g) is in sec.

2*pie *sqrt(l/g) is in sec or second

so both left hand side and right hand side are in second

Hence the equation is dimensionally consistent 


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 2nd, 2015

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