A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T_1 = 4\mathrm{~s}$. $T_2$ would be its time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation [$R =$ radius of earth]:\\
(1) $2\mathrm{~T}_1 = \mathrm{T}_2$\\
(2) $2\mathrm{~T}_1 = 3\mathrm{T}_2$\\
(3) $\mathrm{T}_1 = \mathrm{T}_2$\\
(4) $3\mathrm{T}_1 = 2\mathrm{T}_2$