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# Physics AS Level Homework watch

1. Check each of the following equations for homogeneity:
(a) The periodic time (T) of a simple pendulum of length (l) is given by
T=2π√l/g where (g) is the acceleration due to gravity
3. There's no question here?
4. (Original post by Kozmo)
There's no question here?
You have to write both sides using base quantities to see if they are homogeneous
5. The question is asking to:
equate T in seconds=blah blah blah using base units.
If the overall outcome of the equation is the same, then they are homogeneous. If you are having doubts, check the spoiler below.
Spoiler:
Show
for your's reference. base unit for T is s, base unit for g(acceleration) is m/s^2 or ms^-2, The length is in meters(m).
s= 2pi*(squareroot of m/ms^-2, m get divided by m, so it get canceled)
s= 2pi*(sqroot s^2, as s^-2 gets inversed it changes to s^2)
to remove sq root, square both sides and you get, S^2=S^2.
LHS=RHS so eqn is homogeneous.
6. (Original post by Azhar Rana)
equate T in seconds=blah blah blah using base units.
If the overall outcome of the equation is the same, then they are homogeneous. If you are having doubts, check the spoiler below.
Spoiler:
Show
for your's reference. base unit for T is s, base unit for g(acceleration) is m/s^2 or ms^-2, The length is in meters(m).
s= 2pi*(squareroot of m/ms^-2, m get divided by m, so it get canceled)
s= 2pi*(sqroot s^2, as s^-2 inverse in s^2)
to remove sq root, square both sides and you get, S^2=S^2.
LHS=RHS so eqn is homogeneous.
Thank you so much!
I understand how to do most of it now and the concept of homogeneous . I am a bit confused to how the s^-2 becomes s^2 on the RHS please could you explain it further
7. (Original post by wallflower...)
Thank you so much!
I understand how to do most of it now and the concept of homogeneous . I am a bit confused to how the s^-2 becomes s^2 on the RHS please could you explain it further
It was 1/(s^-2) on the right side, according to the rule of indices, if you raise the denominator in place of numerator, you will do zero power minus (-2) of s so it becomes S^2.

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