TrojanPoem
  • TrojanPoem
Verify if this equation is true based on physics dimensions : T = 2 pi sqrt(l/g) As T = time, l = length , g = gravity
Physics
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SOLVED
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katieb
  • katieb
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Michele_Laino
  • Michele_Laino
hint: we have: \[\sqrt {\frac{l}{g}} = \sqrt {\frac{{{\text{meters}}}}{{{\text{meters/second}}{{\text{s}}^{\text{2}}}}}} \]
TrojanPoem
  • TrojanPoem
I've solved it and got T^-1 as the dimension. The problem is , I can't find which answer is correct a) correct b) correct according to dimensions c) wrong d) wrong according to dimensions d or c ? and why ?
Michele_Laino
  • Michele_Laino
it is correct! namely option a)

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TrojanPoem
  • TrojanPoem
why ?
TrojanPoem
  • TrojanPoem
Ops
Michele_Laino
  • Michele_Laino
a good method is to start from the differential equation of the motion of the pendulum
TrojanPoem
  • TrojanPoem
m/m/s^2 = sqrt(s^2)
TrojanPoem
  • TrojanPoem
But why b is wrong ?
Michele_Laino
  • Michele_Laino
yes! it is correct, nevertheless your reasoning is not able to justify the presence of the coefficient \(2 \pi\) option b) is wrong since we have the correct formula, and the dimensional analysis can not say anything on possible numerical coefficients which may accompany the various formulas
TrojanPoem
  • TrojanPoem
we cannot check if 2 pi is correct therefore b is correct
Michele_Laino
  • Michele_Laino
in other words, using the dimensional analysis I am able to write this: \[T \propto \sqrt {\frac{l}{g}} \]
TrojanPoem
  • TrojanPoem
Yeah, so correct according to dimension ?
Michele_Laino
  • Michele_Laino
no, since you have this formula: \[T = 2\pi \sqrt {\frac{l}{g}} \]
TrojanPoem
  • TrojanPoem
a or b ?
Michele_Laino
  • Michele_Laino
I think it is option a)
TrojanPoem
  • TrojanPoem
Doesn't a mean "We are fully sure that the equation dimensions are correct, constants are correct" ?
Michele_Laino
  • Michele_Laino
this formula: \[T \propto \sqrt {\frac{l}{g}} \] is correct according to dimensions
TrojanPoem
  • TrojanPoem
so if the constant is not written it's correct according to dimensions if it's written , just correct ?
Michele_Laino
  • Michele_Laino
yes!
TrojanPoem
  • TrojanPoem
THANKS.

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