Standard length – second’s pendulum What is the approximate length of a second’s pendulum at standard gravity (period ≈ 2 s), expressed in centimeters?

Introduction / Context:A second’s pendulum is a simple pendulum whose period is about 2 seconds. Its length provides a classic calibration for early clocks and an instructive example of the small-angle pendulum formula.

Given Data / Assumptions:

• Target period T ≈ 2 s.
• Small-angle approximation holds: T = 2π√(L/g).
• Standard gravity g ≈ 9.81 m/s^2 at sea level at mid-latitudes.

Concept / Approach:Rearrange the period formula to find the length L that yields T = 2 s. Convert meters to centimeters to compare with options.

Step-by-Step Solution:

Verification / Alternative check:Local variations in g change L slightly (about ±0.3%), but the standard textbook value remains ≈ 99.39 cm.

Why Other Options Are Wrong:

• 94.9 cm, 100 cm, 101 cm: outside the accepted range for standard gravity with small-angle motion.

Common Pitfalls:Using g = 10 m/s^2 for estimates gives L ≈ 1.013 m (≈ 101.3 cm), which is a rough approximation and not the standard precise value.

Final Answer:99.4 cm