A simple pendulum completes 20 vibrations
in 43 seconds Calculate the length of
the pendulum. Take g = 9.8 m/s²
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Answers
Answer:
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Explanation:
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Concept:
Time period of simple pendulum: The time taken by the pendulum to complete one oscillation or vibration is called its time period. It is given by,
T = 2π √(l/g)
where T = Time period of the pendulum
l = Length of the pendulum
g = Acceleration due to gravity
Time period is also given by,
T = Total time taken/Number of oscillations
Given:
Time taken by the pendulum to complete 20 vibrations = 43 s
Acceleration due to gravity, g = 9.8 m/s²
Find:
The length of the pendulum.
Answer:
The length of the pendulum is 1.15 m.
Solution:
Time taken by the pendulum to complete 20 vibrations = 43 s
Time taken by the pendulum to complete 1 vibration, T = 43/20 s
= 2.15 s
∴ Time period of the pendulum = T = 2.15 s
Let the length of the pendulum be l.
Time period is given by,
T = 2π √(l/g) -------------------------- (i)
Putting the values of T and g in (i), we get
2.15 = 2(3.14) √(l/9.8)
2.15 = 6.28 √(l/9.8)
√l/9.8) = 2.15/6.28
√(l/9.8) = 0.3424
Squaring both sides we get,
[√l/9.8]² = (0.3424)²
l/9.8 = 0.1172
l = 0.1172 × 9.8
l = 1.15 m
Hence, the length of the pendulum is l = 1.15 m.
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