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# Physics As level Watch

1. Attachment 503891503893T=2π squareroot(1/g)
T=2π squareroot(m/k)
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2. Pls help me fast
3. Do they all have the same units?
4. Please.... I'm doing OCR B at AS level and am looking for good revision sites. I have the CGP book but as everyone can guess.. I need an A so that my school write a fantastic reference
5. (Original post by Kyx)
Do they all have the same units?
No they don't
6. Pls hurry guys, I need to complete it tomorrow. (The symbols have their usual meaning) for example m=mass T=seconds

for these dimensional homogeneity questions you have to think in terms of the dimension rather than the unit system...
L is length
T is time (not seconds, seconds is the SI unit for measuring time)
M is mass

so for
a) T=2π (l/g)1/2

you can kick out the 2π immediately because it's dimensionless

T=(l/g)1/2
T2=l/g

now start to put it into the dimensional notation
the dimension of T is T
the dimension of l is L
the dimension of g in basic dimensions (and the dimension of any acceleration) is L T-2 (might help to think about the units acceleration is measured in)

so in dimensional notation we've got
T2=L / L T-2

cancel the Ls
T2=1/T-2
so
T2=T2
T=T ...which is what we're asked for.

NB not all constants are dimensionless so you've got to include the dimensions of (for example) spring constants & the gravitational constant.

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Updated: February 15, 2016
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