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