Dimensional analysis and exponents

[addedline8]

I decided to take physics this year, my senior year in high school, and my teacher has decided he isn't going to explain things before he assigns us homework. Any and all help is appreciated.

1. The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is L and the acceleration of gravity is g, then T is given by:
2. T = 2 (pi) L^p g^q
3. T = 2 (pi) L^p (L/T²)^q

Find the powers p and q required for dimensional consistency.

 

[bp_psy]

Hint. L is in meters, g is in meter/second^2 and period T is in seconds. Now just do the algebra.

 

[PeterO]

I decided to take physics this year, my senior year in high school, and my teacher has decided he isn't going to explain things before he assigns us homework. Any and all help is appreciated.

1. The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is L and the acceleration of gravity is g, then T is given by:



2. T = 2 (pi) L^p g^q



3. T = 2 (pi) L^p (L/T²)^q

Find the powers p and q required for dimensional consistency.

keep going the way you have started..

T = 2 (pi) L^p (L/T²)^q

T = 2 (pi) L^p L^q/T^2q

T = 2 (pi) L^p+q.T ^-2q

Now compare dimensions left and right.

What must -2q equal?

What must p+q equal?

 

[addedline8]

Thanks a lot guys. I appreciate the help.