A pendulum swings with a period of 2 seconds. What is the length of the pendulum

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Question: A pendulum swings with a period of 2 seconds. What is the length of the pendulum? (Take g = 10 m/s²)

Options:

Correct Answer: 2 m

Solution:

Using the formula T = 2π√(l/g), we have l = (T² * g)/(4π²) = (2² * 10)/(4π²) = 1 m.

A pendulum swings with a period of 2 seconds. What is the length of the pendulum? (Take g = 10 m/s²)

A pendulum swings with a period of 2 seconds. What is the length of the pendulum? (Take g = 10 m/s²)

Step 1: Identify the given information. The period (T) of the pendulum is 2 seconds, and the acceleration due to gravity (g) is 10 m/s².
Step 2: Write down the formula for the period of a pendulum: T = 2π√(l/g).
Step 3: Rearrange the formula to solve for the length (l): l = (T² * g) / (4π²).
Step 4: Substitute the values into the formula. First, calculate T²: 2² = 4.
Step 5: Now substitute T² and g into the formula: l = (4 * 10) / (4π²).
Step 6: Simplify the equation: l = 40 / (4π²).
Step 7: Further simplify: l = 10 / π².
Step 8: Calculate the numerical value of l. Using π ≈ 3.14, π² ≈ 9.86, so l ≈ 10 / 9.86 ≈ 1.01 m.
Step 9: Round the answer to a reasonable precision. The length of the pendulum is approximately 1 m.

Pendulum Motion – The relationship between the period of a pendulum and its length, derived from the formula T = 2π√(l/g).
Gravitational Acceleration – Understanding the effect of gravitational acceleration (g) on the pendulum's motion.
Mathematical Manipulation – Rearranging formulas to solve for unknown variables, in this case, the length of the pendulum.