Answer to Question #97957 in Classical Mechanics for Surej
2019-11-03T16:46:38-05:00
A simple pendulum of length 1m makes 400 complete oscillations in 8s at a certain place. If another pendulum makes 100 complete oscillation in 1s at the same place.
Find the length of the second pendulum.
1
2019-11-04T10:39:41-0500
The period:
T = 2 π l g T=2\pi\sqrt{\frac{l}{g}} T = 2 π g l
T 1 = 8 400 = 0.02 s , T 2 = 1 100 = 0.01 s T_1=\frac{8}{400}=0.02\ s,T_2=\frac{1}{100}=0.01\ s T 1 = 400 8 = 0.02 s , T 2 = 100 1 = 0.01 s
Thus,
l 2 = l 1 ( T 2 T 1 ) 2 = 1 ( 0.02 0.01 ) 2 = 4 m l_2=l_1\left(\frac{T_2}{T_1}\right)^2=1\left(\frac{0.02}{0.01}\right)^2=4\ m l 2 = l 1 ( T 1 T 2 ) 2 = 1 ( 0.01 0.02 ) 2 = 4 m
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