Question

Find the length of the pendulum whose time period is 2 s.
(Given: g=9.8 m/s2)
(a) 0.99 m
(b) 0.98 m
(c) 0.1 m
(d) 1.01 m​

Answer 1

Given :

▪ Time period of simple pendulum = 2s

▪ Acceleration due to gravity = 9.8m/s²

To Find :

▪ Length of the simple pendulum.

Formula :

↗ Time requires to complete an oscillation is called as time period.

↗ Formula of time period of a simple pendulum in terms of length of pendulum and gravitational acceleration is given by

$\bigstar\:\underline{\boxed{\bf{\red{T=2\pi\sqrt{\dfrac{L}{g}}}}}}$

• T denotes time period
• L denotes length
• g denotes gravitational acc.

Calculation :

$\dashrightarrow\sf\:T=2\pi\sqrt{\dfrac{L}{g}}\\ \\ \dashrightarrow\sf\:L=\dfrac{T^2\times g}{4\pi^2}\\ \\ \dashrightarrow\sf\:L=\dfrac{(2)^2\times 9.8}{4(3.14)^2}\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{L=0.99m}}}}\:\gray{\bigstar}$

⚽ Second pendulum is the simple pendum, having time period of 2 second. Its effective length is 99.992cm or approximate one metre on earth.

Answer 2

$\large{\red{ \bf{ \underline {\underline{Answer}}}}} \\ \\ \purple{ \sf{\mapsto 0.99}} \\ \\ \mathrm{\green{ \underline{Given}}} \\ \\ \sf{ \rightsquigarrow Time\: Period=2\:sec} \\ \\ \sf{ \rightsquigarrow Gravity=9.8\:m/s}\\ \\ \mathrm {\blue{ \underline{ To \: Find}}} \\ \\ \sf{ \rightsquigarrow Length\;of\: the\:pendulum\:=\:?}$

• According To Given Question

$\sf{T = 2\pi \: \sqrt{ \frac{1}{g} \:} } \\ \\ \sf{ \implies {T}^{2} } = 4 {\pi}^{2} \frac{l}{g} \\ \\ \sf{ \implies L = \frac{ {gt}^{2} }{ {4\pi}^{2} } } \\ \\ \sf{ \implies \frac{9.8 \times 2 \times 2}{4 \times ( {3.14)}^{2} } } \\ \\ \sf{ \implies 0.9939} \\ \\ \sf \purple{ \implies} \purple{ \underline{ \boxed{ \sf{ \backsimeq 0.99 \: m}}}} \:\LARGE{ \pink {\dag}}$