Consider the statements:

Statement I: The universal gravitational constant G is important because it determines the strength of one of the four forces in nature.

 Statement II: By knowing G an accurate value for Earth's mass could finally be obtained.

From the above statements, choose the correct answer from the options given below

Statement I is true: The universal gravitational constant ($G$) is the proportionality constant in Newton's law of universal gravitation. It dictates the exact strength of gravity, which is one of the four fundamental forces of nature (alongside electromagnetism, the strong nuclear force, and the weak nuclear force).Statement II is true: Before $G$ was accurately measured, scientists could only determine the relative masses of planets, but not their absolute masses. We knew the acceleration due to gravity ($g$) and the radius of the Earth ($R$), but without $G$, the Earth's mass ($M$) remained a mystery.

How knowing G solved the Earth's mass

Newton's law relates the surface gravity of Earth ($g$) to its mass ($M$) and radius ($R$) with the following formula:$$g = \frac{G \cdot M}{R^2}$$Rearranging this formula to solve for the Earth's mass gives us:$$M = \frac{g \cdot R^2}{G}$$Because $g$ (approx $9.8 \text{ m/s}^2$) and $R$ (approx $6,371 \text{ km}$) were already known, finding the value of $G$ was the final missing puzzle piece.

In 1798, the scientist Henry Cavendish performed a brilliant and highly sensitive experiment using a torsion balance to measure the tiny gravitational attraction between lead spheres. This experiment essentially yielded the value of $G$ (currently known as $6.674 \times 10^{-11} \text{ N}\cdot\text{m}^2/\text{kg}^2$), which famously allowed Cavendish to "weigh the Earth."