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A simple pendulum oscillates with a period of 2 seconds. What is the length of t

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Question: A simple pendulum oscillates with a period of 2 seconds. What is the length of the pendulum? (2021)

Options:

  1. 0.5 m
  2. 1 m
  3. 2 m
  4. 4 m

Correct Answer: 1 m

Exam Year: 2021

Solution: 

The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T^2 * g) / (4π^2). Using g = 9.8 m/s² and T = 2 s, we find L = (2^2 * 9.8) / (4π^2) ≈ 1 m.

A simple pendulum oscillates with a period of 2 seconds. What is the length of t

Practice Questions

Q1
A simple pendulum oscillates with a period of 2 seconds. What is the length of the pendulum? (2021)
  1. 0.5 m
  2. 1 m
  3. 2 m
  4. 4 m

Questions & Step-by-Step Solutions

A simple pendulum oscillates with a period of 2 seconds. What is the length of the pendulum? (2021)
  • Step 1: Understand the formula for the period of a simple pendulum, which is T = 2π√(L/g).
  • Step 2: Rearrange the formula to solve for L (length of the pendulum). The rearranged formula is L = (T^2 * g) / (4π^2).
  • Step 3: Identify the values needed for the calculation. We have T = 2 seconds and g = 9.8 m/s².
  • Step 4: Substitute the values into the rearranged formula: L = (2^2 * 9.8) / (4π^2).
  • Step 5: Calculate 2^2, which is 4.
  • Step 6: Multiply 4 by 9.8 to get 39.2.
  • Step 7: Calculate 4π^2. First, find π (approximately 3.14), then square it to get about 9.86, and finally multiply by 4 to get approximately 39.44.
  • Step 8: Divide 39.2 by 39.44 to find L. This gives approximately 1 meter.
  • Simple Pendulum Period – The relationship between the period of a simple pendulum and its length, derived from the formula T = 2π√(L/g).
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