What’s the smallest gravitational force you can produce between the two masses? F =
The correct answer and explanation is:
To calculate the smallest gravitational force between two masses, we use Newton’s Law of Universal Gravitation: F=G⋅m1⋅m2r2F = \frac{G \cdot m_1 \cdot m_2}{r^2}
Where:
- FF is the gravitational force,
- GG is the gravitational constant, 6.674×10−11 N\cdotpm2/kg26.674 \times 10^{-11} \, \text{N·m}^2/\text{kg}^2,
- m1m_1 and m2m_2 are the two masses,
- rr is the distance between the centers of the masses.
Smallest Gravitational Force
There is no absolute minimum gravitational force, but we can produce an extremely small one by choosing:
- Very small masses, like subatomic particles (e.g., protons),
- Large separation distance.
Example:
Let’s calculate the gravitational force between two protons separated by 1 meter.
- Mass of a proton, mp=1.6726×10−27 kgm_p = 1.6726 \times 10^{-27} \, \text{kg}
- Distance, r=1 mr = 1 \, \text{m}
F=(6.674×10−11)⋅(1.6726×10−27)212F = \frac{(6.674 \times 10^{-11}) \cdot (1.6726 \times 10^{-27})^2}{1^2} F=(6.674×10−11)⋅(2.797×10−54)1F = \frac{(6.674 \times 10^{-11}) \cdot (2.797 \times 10^{-54})}{1} F≈1.867×10−64 NF \approx 1.867 \times 10^{-64} \, \text{N}
Explanation (300 Words)
Gravitational force exists between all objects with mass. It is extremely weak compared to other fundamental forces—especially at small scales. Newton’s Universal Law shows that gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them.
When dealing with microscopic objects such as protons or electrons, their mass is so small that the gravitational force becomes minuscule—virtually undetectable with current instruments. In our example, we used two protons (each with a mass of approximately 1.6726×10−271.6726 \times 10^{-27} kg) and placed them 1 meter apart. The gravitational attraction between them is calculated to be roughly 1.867×10−641.867 \times 10^{-64} newtons—a force so small it has no measurable effect in real-world experiments.
This shows that although gravity is universal, it is significant only when at least one of the interacting masses is large (like Earth). At atomic or subatomic scales, other forces like electromagnetic or nuclear forces dominate.
Theoretically, the gravitational force can be made even smaller by using smaller particles or increasing the distance further. However, due to the quantized nature of particles and limits in physical separation in practical experiments, there is a limit to what can be produced or measured.
Thus, the smallest gravitational force possible is incredibly tiny and only meaningful in theoretical contexts or extremely sensitive physics research.