Question

(a) What is the ratio of the strength of the gravitational force to that of the strong nuclear force?

(b) What is the ratio of the strength of the gravitational force to that of the weak nuclear force?

(c) What is the ratio of the strength of the gravitational force to that of the electromagnetic force? What do your answers imply about the influence of the gravitational force on atomic nuclei?

Short answer

(a) The strength of gravitational force relative to strong nuclear force is${10}^{-38}$.

(b) The strength of gravitational force relative to weak nuclear force is${10}^{-25}$.

(c) The strength of gravitational force relative to electromagnetic force is ${10}^{-36}$.

Step-by-step solution

(a) Strength of gravitational force relative to the strong nuclear force

Gravitational force is generally the force of gravity. These forces are attractive and dormant in nature. It determines the motion of stars, galaxies, planets, and moons. Whereas nuclear forces play a vital role in the structure of matter, and they act over a short-range. These forces help in determining the stability of nuclei.

The relative strength of the gravitational force is of the order of,${10}^{-38}$whereas the relative strength of the strong nuclear force is 1.

Determine the ratio of gravitational force to the strong nuclear force as:

$$\begin{gathered} \frac{F_g}{F_{N,s}}=\frac{{10}^{-38}}{1} \\ ={10}^{-38} \end{gathered}$$

Here,$F_g$is the gravitational force, and$F_{N,s}$is the strong nuclear force.

Hence, the strength of gravitational force relative to strong nuclear force is ${10}^{-38}$.

(b) Strength of gravitational force relative to the weak nuclear force.

The relative strength of the weak nuclear force is${10}^{-13}$.

Determine the ratio of gravitational force to the weak nuclear force as:

$$\begin{gathered} \frac{F_g}{F_{N,w}}=\frac{{10}^{-38}}{{10}^{-13}} \\ ={10}^{-25} \end{gathered}$$

Here,$F_{N,w}$is the weak nuclear force.

Hence, the strength of gravitational force relative to weak nuclear force is ${10}^{-25}$.

(c) Strength of gravitational force relative to the electromagnetic force

Electromagnetic forces are long-range forces that act over large distances. These forces can be attractive or repulsive in nature.

The relative strength of the electromagnetic force is 10^-2.

Determine the ratio of gravitational force to the electromagnetic force as:

$$\begin{gathered} \frac{F_g}{F_{electric}}=\frac{{10}^{-38}}{{10}^{-2}} \\ ={10}^{-36} \end{gathered}$$

Here,$F_{electric}$ is the electromagnetic force.

Hence, the strength of gravitational force relative to electromagnetic force is ${10}^{-36}$.