The time period of a simple pendulum is T. When the length is increased by 10 cm,its period is $T_1$. When the length is decreased by 10 cm, its period is $T_2$. Then, the relation between $T,T_1\;and T_2$ is :

Question

$$\begin {array} {1 1} (a)\;\frac{2}{T^2}=\frac{1}{T_1^2}+\frac{1}{T_2^2} & \quad (b)\;\frac{2}{T^2}=\frac{1}{T_1^2}+\frac{1}{T_2^2} \\ (c)\;2T^2=T_1^2T_2^2 & \quad (d)\;2T^2=T_1^2-T_2^2 \end {array}$$