Answer
The acceleration due to gravity on this planet is $6.04m/s^2$
Work Step by Step
In a simple pendulum, $$\frac{2\pi}{T}=\sqrt{\frac{g}{L}}$$ $$\frac{g}{L}=\frac{4\pi^2}{T^2}$$ $$g=\frac{4\pi^2L}{T^2}$$
Here, the pendulum's length $L=1.2m$. The pendulum finishes $100$ vibrations in $280s$, so the motion's period $T=\frac{280s}{100rev}=2.8s$
So the acceleration due to gravity on this planet is $$g=6.04m/s^2$$
