Answer
$\frac{L_2}{L_1} = 1.11$
Work Step by Step
We can find an expression for $L_1$:
$T_1 = 2\pi~\sqrt{\frac{L_1}{g}}$
$(\frac{T_1}{2\pi})^2 = \frac{L_1}{g}$
$L_1 = \frac{T_1^2~g}{(2\pi)^2}$
We can find an expression for $L_2$:
$T_2 = 2\pi~\sqrt{\frac{L_2}{g}}$
$(\frac{T_2}{2\pi})^2 = \frac{L_2}{g}$
$L_2 = \frac{T_2^2~g}{(2\pi)^2}$
We can find the value of the ratio $\frac{L_2}{L_1}$:
$\frac{L_2}{L_1} = \frac{\frac{T_2^2~g}{(2\pi)^2}}{\frac{T_1^2~g}{(2\pi)^2}}$
$\frac{L_2}{L_1} = \frac{T_2^2}{T_1^2}$
$\frac{L_2}{L_1} = \frac{(1.00~s)^2}{(0.950~s)^2}$
$\frac{L_2}{L_1} = 1.11$
