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A pendulum swings to and fro. If the length of the pendulum is 2 m, what is the
A pendulum swings to and fro. If the length of the pendulum is 2 m, what is the time period of the pendulum? (Take g = 10 m/s²)
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Practice Questions
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Q1
A pendulum swings to and fro. If the length of the pendulum is 2 m, what is the time period of the pendulum? (Take g = 10 m/s²)
1.4 s
2.0 s
1.0 s
3.0 s
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Time period T = 2π√(l/g) = 2π√(2/10) = 2π√(0.2) ≈ 2.0 s.
Questions & Step-by-step Solutions
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Q
Q: A pendulum swings to and fro. If the length of the pendulum is 2 m, what is the time period of the pendulum? (Take g = 10 m/s²)
Solution:
Time period T = 2π√(l/g) = 2π√(2/10) = 2π√(0.2) ≈ 2.0 s.
Steps: 8
Show Steps
Step 1: Identify the formula for the time period of a pendulum, which is T = 2π√(l/g).
Step 2: Substitute the given values into the formula. Here, l (length of the pendulum) is 2 m and g (acceleration due to gravity) is 10 m/s².
Step 3: Replace l and g in the formula: T = 2π√(2/10).
Step 4: Simplify the fraction inside the square root: 2/10 = 0.2.
Step 5: Now the formula looks like this: T = 2π√(0.2).
Step 6: Calculate the square root of 0.2, which is approximately 0.447.
Step 7: Multiply 2π by 0.447 to find the time period T.
Step 8: The final calculation gives T ≈ 2.0 seconds.
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