dimensionally consistent.

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Science

Description

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. 

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Explanation & Answer

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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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Anonymous
This is great! Exactly what I wanted.

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