Question

2. What is the length of a pendulum that h
as a period of 0.500 s?
​

Answer 1

Answer:

Given:

Time period of pendulum = 0.5 seconds.

To find:

Length of the pendulum.

Calculation:

For any simple pendulum having length l , the time period is given as :

$\boxed{ \red{ \sf{T = 2\pi \sqrt{ \dfrac{l}{g} }}}}$

Putting in a the available data :

$\sf{ \implies 2\pi \sqrt{ \dfrac{l}{g} } = 0.5}$

$\sf{ \implies \sqrt{ \dfrac{l}{g} } = \dfrac{0.5}{2\pi} }$

$\sf{ \implies \sqrt{ \dfrac{l}{g} } = 0.0795}$

$\sf{ \implies \dfrac{l}{g} = 0.00632}$

Considering g = 10 m/s² at that point on the surface of Earth :

$\sf{ \implies l = 0.00632 \times g}$

$\sf{ \implies l = 0.00632 \times 10}$

$\sf{ \implies l = 0.0632 \: m}$

So final answer :

$\boxed{ \green{ \sf{ \star \: l = 0.0632 \: m}}}$

Answer 2

$\blue{\underline{ \huge{ \blue{\boxed{ \mathfrak{\fcolorbox{red}{orange}{\purple{Answer}}}}}}}} \\ \\ \dagger \: \boxed{ \red{ \rm{Given}}} \\ \\ \mapsto \rm \: time \: period \: of \: simple \: pendulum \: (T) = 0.5 \: s \\ \\ \dagger \: \boxed{ \red{ \rm{To \: Find}}} \\ \\ \mapsto \rm \: length \: of \: simple \: pendulum \: (l) \\ \\ \dagger \: \boxed{ \rm{ \red{Formula}}} \\ \\ \mapsto \rm \: time \: period \: of \: simple \: pendulum \: is \: given \: by \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \star \: \underline{ \boxed{ \bold{ \sf{ \pink{T = 2\pi \sqrt{ \frac{l}{g} }}}}}} \: \star$

For Calculation, please see the attached image...