Given that the time period of the pendulum is T = 2 s
Let the length of the pendulum be L.
The new length of the pendulum is 2L
The relation between length and time period is
[tex]T=2\pi\sqrt[]{\frac{L}{g}}[/tex]Here, g = 9.8 m/s^2 is the acceleration due to gravity.
The length will be
[tex]\begin{gathered} L=\frac{T^2}{4\pi^2}\times g \\ =\frac{(2)^2}{4\times(3.14)^2}\times9.8 \\ =\text{ 0.994 m} \end{gathered}[/tex]The new length will be
[tex]\begin{gathered} 2L=2\times0.994 \\ =1.988\text{ m} \end{gathered}[/tex]The new length will be 1.988 m
The new time period will be
[tex]\begin{gathered} T^{\prime}=2\pi\sqrt[]{\frac{2L}{g}} \\ =2\times3.14\times\sqrt[]{\frac{1.988}{9.8}} \\ =2.83\text{ s} \end{gathered}[/tex]Thus, the new time period is 2.83 s
