MCAT Physics: Find Rod Length After 20% Decrease in Pendulum Period

[caviar]

Homework Statement

The length of the rod of a certain pendulum is decreased, and the period then decreases by 20%. By how much was the rod length decreased?

Homework Equations

T=2π√(l/g)
T=period
l=length of the rod
g=acceleration due to gravity

The Attempt at a Solution

I know how to solve the problem, I just don't know how to do the math to solve for l (length).

 

[bigfooted]

If you know how to solve the problem, what is then the difficulty that you have?

you have the relevant equation that gives you the period as function of length. But you want to have an expression for the length as function of the period. And then you want an expression that gives you the length for a 20% longer period.

 

[Hollumber]

I don't understand what you are asking.

Are you saying you don't know how to solve T = 2pi*sqrt(l/g) for l?
Because this is basic algebra: l = g*(T/2pi)^2

 

[caviar]

Sorry for the confusion, yeah I forgot how to do basic algebra and don't understand why this is the answer: l=4π^2gT^2, and not this l=gT^2/4π^2 (what you said and what I think it is too)?

Either way you can still find the answer because when you multiply T by 0.80, you multiply l by 0.64 (0.8^2). So, the length (l) decreases by 36% (1-0.64).

 

[Hollumber]

Mm, I wouldn't trust that. Must be some sort of misprint or mistake...unless my 6th grade teacher was wrong all this time