Your grandfather clock\'s pendulum has a length of 0.9930 m. If the clock runs s
ID: 1620361 • Letter: Y
Question
Your grandfather clock's pendulum has a length of 0.9930 m. If the clock runs slow and loses 26 s per day, how should you adjust the length of the pendulum?
Note: due to the precise nature of this problem you must treat the constant g as unknown (that is, do not assume it is equal to exactly 9.80 m/s2). Express your answer to two significant figures and include the appropriate units. Enter positive value in case of increasing length of the pendulum and negative value in case of decreasing length of the pendulum.
Explanation / Answer
time period of pendulum T = 2*pi*sqrt(L/g)
1 day = 24*60*60 = 86400 s
let the pendulum take N oscillation for one day
N*T = 86400 s
I fthe pendulum loses 26s per day
N*T' = (86400-26) = 86374 s
T/T' = 86400/86374
sqrt(L/L') = 86400/86374
sqrt(0.993/L') = 86400/86374
L' = 0.9924 m
L' < L
length is decreased
decrease in length = L - L' = 0.9930 - 0.9924 = 0.0006 m <<<<------answer
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