Answer:
[tex]\frac{g_{2}}{g_{1}} = \frac{1}{4}[/tex]
Explanation:
The period of the simple pendulum is:
[tex]T = 2\pi\cdot \sqrt{\frac{l}{g} }[/tex]
Where:
[tex]l[/tex] - Cord length, in m.
[tex]g[/tex] - Gravity constant, in [tex]\frac{m}{s^{2}}[/tex].
Given that the same pendulum is test on each planet, the following relation is formed:
[tex]T_{1}^{2}\cdot g_{1} = T_{2}^{2}\cdot g_{2}[/tex]
The ratio of the gravitational constant on planet CornTeen to the gravitational constant on planet Earth is:
[tex]\frac{g_{2}}{g_{1}} = \left(\frac{T_{1}}{T_{2}} \right)^{2}[/tex]
[tex]\frac{g_{2}}{g_{1}} = \left(\frac{2\,s}{4\,s} \right)^{2}[/tex]
[tex]\frac{g_{2}}{g_{1}} = \frac{1}{4}[/tex]
