Respuesta :
Given data:
Length of peldulum is,
[tex]l_1=L[/tex]Period of pendulum is,
[tex]T_1=T[/tex]New period of pendulum is,
[tex]T_2=3T[/tex]Formula:
Formula of period of pedulum is as follows:
[tex]T=2\Pi\sqrt[]{\frac{l}{g}}[/tex]For old period of pendulum above equation becomes as follows:
[tex]T=2\Pi\sqrt[]{\frac{L}{g}}[/tex]Taking square of above equation,
[tex]\begin{gathered} T^2=4\Pi^2\frac{L}{g} \\ L=T^2g\frac{1}{4\Pi}\text{ ..}.(1) \end{gathered}[/tex]Now, for new period of pendulum,
[tex]T_2=2\Pi\sqrt[]{\frac{L_2}{g}}[/tex]Taking square of above equation,
[tex]T_2=3T^{}_{}_{}[/tex]Hence,
[tex]\begin{gathered} (3T)^2=4\Pi^2\frac{L_2}{\text{g}}\ldots(2) \\ L_2=9T^2g\frac{1}{4\Pi}\ldots(3) \end{gathered}[/tex]Taking ratio of equation-(3) and equation-(1),
[tex]\begin{gathered} \frac{L_2}{L}=9T^2g\frac{1}{4\Pi}\times\frac{1}{T^2g}4\Pi \\ \frac{L_2}{L}=9 \\ L_2=9L \end{gathered}[/tex]Therefore, Length of pendulum should be 9L for the period to be 3T seconds.
