Physics

Problem

A pendulum’s time period is experimentally measured as

T

and the local acceleration due to gravity is

g

. Which one of the following expressions correctly gives the length

L

of the pendulum in SI units? a)

L = \dfrac{g T^{2}}{8\pi^{2}}

L = \dfrac{g T^{2}}{4\pi^{2}}

L = \dfrac{g T^{2}}{2\pi}

L = \dfrac{g T^{2}}{\pi^{2}}

Intuitive explanation

The key insight is recognizing that the pendulum's period formula $T = 2\pi\sqrt{\frac{L}{g}}$ directly connects all three quantities. To find $L$ , you need to algebraically isolate it by squaring both sides and rearranging—a straightforward inverse operation. Once you do, you'll have $L$ expressed in terms of the measured period $T$ and local gravity $g$ , giving you the pendulum's length in meters.

Intuitive explanation

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