Question

Find the length of a simple pendulum which completes 6 oscillations in 5 seconds. ​

Answer 1

Given:

A simple pendulum completes 6 oscillations in 5 seconds.

To find:

Length of the pendulum.

Calculation:

Time period of a pendulum is defined as the time taken to complete one full oscillation.

$\therefore \: time \: period = t = \dfrac{5}{6} \: sec$

Now , general expression for time period of a simple pendulum is :

$\boxed{t = 2\pi \sqrt{ \dfrac{l}{g} } }$

Putting available values:

$= > \dfrac{5}{6} = 2\pi \sqrt{ \dfrac{l}{10} }$

$= > \dfrac{5}{12\pi} = \sqrt{ \dfrac{l}{10} }$

$= > \dfrac{l}{10} = \dfrac{25}{144 {\pi}^{2} }$

$= > l = \dfrac{25 \times 10}{144 {\pi}^{2} }$

$= > l = \dfrac{250}{144 {\pi}^{2} }$

$= > l = \dfrac{1.73}{ {\pi}^{2} }$

$= > l \approx 0.175 \: m$

$= > l \approx 17.5 \: cm$

So, final answer is:

$\boxed{ \bf{ \red{l \approx 17.5 \: cm}}}$