Simple Pendulum

Question

Approximate length of simple pendulum with period 2 s (g=10 m/s²)?

RankGuru · Accepted Answer

1. **Fundaμental Formula**: The period of a simple pendulum for small oscillations is $T = 2\pi \sqrt{\frac{L}{g}}$.
2. **Given**: $T = 2$ s and $g = 10 	ext{ m/s}^2$.
3. **Isolate Length (L)**:
   - $2 = 2\pi \sqrt{\frac{L}{10}}$
   - $1 = \pi \sqrt{\frac{L}{10}}$
   - $\frac{1}{\pi} = \sqrt{\frac{L}{10}} \implies \frac{1}{\pi^2} = \frac{L}{10}$.
4. **Numerical Approximation**: Since $\pi^2 \approx 9.87 \approx 10$:
   - $L \approx \frac{10}{10} = 1.0$ m.
5. **Note**: A pendulum with a period of exactly $2$ seconds is called a **Seconds Pendulum**.

Simple Pendulum

Select the correct option:

Solution

🔒 Solution Hidden from View

More simple pendulum Practice Questions

A pendulum clock keeps correct time on Earth, but if it were taken to the Moon where gravity is abou...

A student in a laboratory wants a simple pendulum whose period is exactly 2 seconds using g equal to...

In the simple pendulum experiment for g, a student wants to reduce the fractional error in the resul...

A simple pendulum used to determine acceleration due to gravity has a measured length of 1.0 m and a...

A grandfather clock keeps time using a simple pendulum, and its bob swings with a period of exactly ...

About This Question

Solution