Question

Find the length of a simple pendulum whose time period is 1.8s where g=9.8m/s2

Answer 1

Answer :

➥ The length of a simple pendulum = 0.80 m

Given :

➤ Time period of a simple pendulum (T) = 1.8 sec

➤ Acceleration due to gravity (g) = 9.8 m/s²

To Find :

➤ Length of a simple pendulum (l) = ?

Required Solution :

We can find length of a simple pendulum by using the length of pendulum formula which says T = 2π √l/g,

☃️ So let's find the length of a simple pendulum by using the formula:

As we know that

$\tt{:\implies T = 2 \pi \sqrt{ \dfrac{l}{g} } }$

$\tt{:\implies {T}^{2} = 4{\pi}^{2} + \dfrac{l}{g} }$

$\tt{:\implies l = \dfrac{ {T}^{2} \times g}{4 {\pi}^{2} } }$

$\tt{:\implies l = \dfrac{ {(1.8)}^{2} \times 9.8}{4 \times {(3.14)}^{2} } }$

$\tt{:\implies l = \dfrac{3.24 \times 9.8}{4 \times 9.85} }$

$\tt{:\implies l = \dfrac{31.75}{4 \times 9.85} }$

$\tt{:\implies l = \cancel{\dfrac{31.75}{39.4} }}$

$\bf{:\implies \underline{ \: \: \underline{ \red{ \: \: l = 0.80 \: m \: \: }} \: \: }}$

║Hence, the length of a simple pendulum is 0.80 m║