Question

What is a second pendulum. Define it's effective length​

Answer 1

Answer:

The pendulum whose time period is 2 sec is called second pendulum. its effective length is 1 meter.

Answer 2

$\large \: \:\: \: \: \: \: \: \: \: \: \: \:\underline{\underline{\mathfrak{Answer:}}}$

A second pendulum is a pendulum which have time interval to swing is two seconds. One to move in one direction and another one second to swing in opposite direction.

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$\large \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\underline{\mathfrak{Derivation :}}}$

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

$\\ \\ \small \sf{Where} \begin{cases} \tt{T\ is\ time\ of\ pendulum\ to\ swing} \\ \\ \tt{l\ is\ length\ of\ pendulum} \\ \\ \tt{g\ is\ acceleration\ due\ to\ gravity} \end{cases} \\ \\ \\ \\ \implies \sf{2\ =\ 2\pi \sqrt{\dfrac{l}{9.8}}} \\ \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \dag\: {\underline{\footnotesize{\tt{Square\ both\ the\ sides}}}} \\ \\ \\ \\ \implies \sf{2^2\ =\ \bigg( 2\pi \sqrt{\dfrac{l}{9.8}} \bigg)^2} \\ \\ \\ \\ \implies \sf{\cancel{4}\ =\ \cancel{4} \pi^2\ \times\ \dfrac{l}{9.8}} \\ \\ \\ \\ \implies \sf{1\ =\ (3.14)^2\ \times\ \dfrac{l}{9.8}} \\ \\ \\ \\ \implies \sf{1\ =\ \cancel{9.8}\ \times\ \dfrac{l}{\cancel{9.8}}} \\ \\ \\ \\ \implies \sf{l\ =\ 1\ m} \\ \\ \\ \\ \\ \large \dag \: \: \underline{\boxed{\sf{Length\ =\ 1\ m}}}$