SOLUTION: The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it

Algebra ->  Equations -> SOLUTION: The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it       Log On


   

Question 78467: The period of a simple pendulum is directly proportional to the square root of its length. If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shortened to achieve 1 second period?
a. 1 foot
b. 1.5 foot
c. 2 feet
d. 3 feet
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We have the equation
T=k%2Asqrt%28L%29 "The period of a simple pendulum is directly proportional to the square root of its length"
Substitute L=6 and T=2 and solve for k
2=k%2Asqrt%286%29
2%2Fsqrt%286%29=k%2Across%28sqrt%286%29%2Fsqrt%286%29%29 Divide both sides by sqrt%286%29
So our constant is
k=2%2Fsqrt%286%29
Now the equation becomes
T=2%2Fsqrt%286%29%2Asqrt%28L%29
Now plug in T=1 to solve for L
1=2%2Fsqrt%286%29%2Asqrt%28L%29
1%2F%282%2Fsqrt%286%29%29=sqrt%28L%29 Divide both sides by 2%2Fsqrt%286%29
sqrt%286%29%2F2=sqrt%28L%29 Divide
%28sqrt%286%29%2F2%29%5E2=%28sqrt%28L%29%29%5E2 Square both sides
6%2F4=L
L=3%2F2 reduce
So our length must be 1.5 feet to have a period of 1 second.