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

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Question 83017: 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 shorten to achieve a 1 second period? The answer is multiple choice.
a. 1 foot
b. 1.5 feet
c. 2 feet
d. 3 feet
Found 2 solutions by funmath, josmiceli:
Answer by funmath(2925) About Me  (Show Source):
You can put this solution on YOUR website!
The period (T) of a simple pendulum is directly proportional to the square root of its length (L). If a pendulum has a length of 6 feet and a period of 2 seconds, to what length should it be shorten to achieve a 1 second period? The answer is multiple choice.
a. 1 foot
highlight%28b%29. 1.5 feet
c. 2 feet
d. 3 feet
Directly proportional means multiply, k is the proportionality constant:
T=k%2Asqrt%28L%29, L=6 and T=2, find k
2=k%2Asqrt%286%29
2%2Fsqrt%286%29=k
The formula is
T=%282%2Fsqrt%286%29%29%2Asqrt%28L%29 let T=1 and find L
1=%282%2Fsqrt%286%29%29%2Asqrt%28L%29
%28sqrt%286%29%2F2%29%2A1=%28sqrt%286%29%2F2%29%282%2Fsqrt%286%29%29%2Asqrt%28L%29
sqrt%286%29%2F2=sqrt%28L%29
%28sqrt%286%29%2F2%29%5E2=%28sqrt%28L%29%29%5E2
6%2F4=L
3%2F2=L
L=1.5 feet

Answer by josmiceli(9650) About Me  (Show Source):
You can put this solution on YOUR website!
(b) 1.5 ft
p = period
s = length in ft
k = constant of proportionality
p+=+k%2Asqrt%28s%29
k+=+p%2Fsqrt%28s%29
k+=+2%2Fsqrt%286%29
p = 1 sec
1+=+k%2Asqrt%28s%29
1+=+%282%2Fsqrt%286%29%29%2Asqrt%28s%29
sqrt%28s%29+=+sqrt%286%29+%2F+2
square both sides
s+=+6+%2F+4
s+=+3%2F2
length for a 1 sec period is 1.5 ft answer