Answer
$g = 10.7~m/s^2$
Work Step by Step
We can find the period of the oscillations.
$T = \frac{time}{cycles}$
$T = \frac{136~s}{100~swings}$
$T = 1.36~s$
We can find the value of $g$ on this planet.
$T = 2\pi~\sqrt{\frac{L}{g}}$
$g = \frac{(2\pi)^2~L}{T^2}$
$g = \frac{(2\pi)^2(0.500~m)}{(1.36~s)^2}$
$g = 10.7~m/s^2$