If $R$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g = \pi ^ { 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }$, then the length of the second's pendulum at a height $h = 2R$ from the surface of earth will be:\\
(1) $\frac { 2 } { 9 } \mathrm {~m}$\\
(2) $\frac { 1 } { 9 } \mathrm {~m}$\\
(3) $\frac { 4 } { 9 } \mathrm {~m}$\\
(4) $\frac { 8 } { 9 } \mathrm {~m}$