Question:
Two protons are separated by a distance of 1 nanometer. The magnitudes of gravitational, electromagnetic and strong nuclear forces between them are denoted by $F_G$, $F_E$ and $F_S$ respectively. Select the correct option.
Two protons are separated by a distance of 1 nanometer. The magnitudes of gravitational, electromagnetic and strong nuclear forces between them are denoted by $F_G$, $F_E$ and $F_S$ respectively. Select the correct option.
Show Hint
Remember that the strong nuclear force falls off exponentially with distance ($F_S \propto e^{-r/r_0}$).
At $1\text{ nm}$, it is mathematically much smaller than even the gravitational force, which only falls off as $1/r^2$.
At $1\text{ nm}$, it is mathematically much smaller than even the gravitational force, which only falls off as $1/r^2$.
Updated On: Jun 16, 2026
- $F_E \gt F_G \gt F_S$
- $F_E \gt F_S \gt F_G$
- $F_S \gt F_G \gt F_E$
- $F_S \gt F_E \gt F_G$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The problem asks us to compare the strengths of the three fundamental forces acting between two protons separated by a distance of 1 nanometer ($10^{-9}\text{ m}$).
Step 2: Key Formula or Approach:
We must consider the range and relative strengths of the fundamental forces:
- Electromagnetic force $F_E$ has an infinite range and is very strong between charged particles at atomic scales.
- Gravitational force $F_G$ also has an infinite range but is extremely weak between subatomic particles.
- Strong nuclear force $F_S$ is the strongest force but has an extremely short range (only acts up to $1 - 2\text{ fm}$ or $10^{-15}\text{ m}$).
Step 3: Detailed Explanation:
• The separation distance is $r = 1\text{ nm} = 10^{-9}\text{ m}$.
• At this distance, the strong nuclear force is virtually zero because $1\text{ nm}$ is about a million times larger than its range of influence ($10^{-15}\text{ m}$):
\[ F_S \approx 0 \]
• The electromagnetic force is given by Coulomb's law:
\[ F_E = \frac{k q^2}{r^2} \approx \frac{(9 \times 10^9) \times (1.6 \times 10^{-19})^2}{(10^{-9})^2} \approx 2.3 \times 10^{-10}\text{ N} \]
• The gravitational force is given by Newton's law:
\[ F_G = \frac{G m^2}{r^2} \approx \frac{(6.67 \times 10^{-11}) \times (1.67 \times 10^{-27})^2}{(10^{-9})^2} \approx 1.86 \times 10^{-46}\text{ N} \]
• Comparing these values, we find:
\[ F_E \gt F_G \gt F_S \]
Step 4: Final Answer:
The correct option is $F_E \gt F_G \gt F_S$.
The problem asks us to compare the strengths of the three fundamental forces acting between two protons separated by a distance of 1 nanometer ($10^{-9}\text{ m}$).
Step 2: Key Formula or Approach:
We must consider the range and relative strengths of the fundamental forces:
- Electromagnetic force $F_E$ has an infinite range and is very strong between charged particles at atomic scales.
- Gravitational force $F_G$ also has an infinite range but is extremely weak between subatomic particles.
- Strong nuclear force $F_S$ is the strongest force but has an extremely short range (only acts up to $1 - 2\text{ fm}$ or $10^{-15}\text{ m}$).
Step 3: Detailed Explanation:
• The separation distance is $r = 1\text{ nm} = 10^{-9}\text{ m}$.
• At this distance, the strong nuclear force is virtually zero because $1\text{ nm}$ is about a million times larger than its range of influence ($10^{-15}\text{ m}$):
\[ F_S \approx 0 \]
• The electromagnetic force is given by Coulomb's law:
\[ F_E = \frac{k q^2}{r^2} \approx \frac{(9 \times 10^9) \times (1.6 \times 10^{-19})^2}{(10^{-9})^2} \approx 2.3 \times 10^{-10}\text{ N} \]
• The gravitational force is given by Newton's law:
\[ F_G = \frac{G m^2}{r^2} \approx \frac{(6.67 \times 10^{-11}) \times (1.67 \times 10^{-27})^2}{(10^{-9})^2} \approx 1.86 \times 10^{-46}\text{ N} \]
• Comparing these values, we find:
\[ F_E \gt F_G \gt F_S \]
Step 4: Final Answer:
The correct option is $F_E \gt F_G \gt F_S$.
Was this answer helpful?
0
0
Top NEST Physics Questions
- In the 2024 Olympics, two runners, Noah Lyles and Kishane Thompson, finished the 100.00 m race in 9.784 s and 9.789 s respectively. Assuming that they move with constant speed throughout the race, the distance between the two runners when Noah Lyles touched the finishing line would be closest to:
- The Balmer series of hydrogenic spectral lines refers to an electron transitioning from \(n\geq 3\) to \(n=2\). A hydrogenic atom with atomic number \(Z=24\) undergoes a Balmer transition of the largest possible wavelength. The emitted photon has energy \(E_0\). Another hydrogenic atom with atomic number \(Z=25\) undergoes a similar Balmer transition with emitted photon energy \(E_1\). Then \(|E_1-E_0|\), in eV, is closest to:
- Three positive and two negative charges each of magnitude \(q\) are placed at five of the six vertices of a regular hexagon of side \(R\). The work done to bring a negative charge \(-q\) from infinity to the centre of the hexagon is:
- Consider a metal cylinder of heat capacity \(C\), thermal conductivity \(K\), mass \(m\) and radius \(r\). The combination that will have the dimension of time is:
- The angular speed of the Earth’s rotation is $7.3 \times 10^{-5}\text{ rad}\cdot\text{s}^{-1}$. Take the radius of the Earth at the equator to be $6400\text{ km}$. Then the ratio ($a_c / g$) of the magnitude of the centripetal acceleration $a_c$ at a point on the equator to $g$, is of the order
View More Questions
Top NEST Atomic Structure Questions
- The Balmer series of hydrogenic spectral lines refers to an electron transitioning from \(n\geq 3\) to \(n=2\). A hydrogenic atom with atomic number \(Z=24\) undergoes a Balmer transition of the largest possible wavelength. The emitted photon has energy \(E_0\). Another hydrogenic atom with atomic number \(Z=25\) undergoes a similar Balmer transition with emitted photon energy \(E_1\). Then \(|E_1-E_0|\), in eV, is closest to:
- Let $A$ be the mass number, $Z$ be the atomic number and $N$ be the neutron number of a nucleus. Then the statement which is always true, is
- The electron in the hydrogen atom is in the third excited state. Its potential energy (in eV) is
- The critical electric field required to produce electron-positron pairs depends on the physical constants $h$, $c$, $m_e$ and $e$. Use dimensional analysis and assume that the dimensionless coefficient is of order one. The magnitude of the critical electric field, in SI units, is of the order
Top NEST Questions
- In the 2024 Olympics, two runners, Noah Lyles and Kishane Thompson, finished the 100.00 m race in 9.784 s and 9.789 s respectively. Assuming that they move with constant speed throughout the race, the distance between the two runners when Noah Lyles touched the finishing line would be closest to:
- The Balmer series of hydrogenic spectral lines refers to an electron transitioning from \(n\geq 3\) to \(n=2\). A hydrogenic atom with atomic number \(Z=24\) undergoes a Balmer transition of the largest possible wavelength. The emitted photon has energy \(E_0\). Another hydrogenic atom with atomic number \(Z=25\) undergoes a similar Balmer transition with emitted photon energy \(E_1\). Then \(|E_1-E_0|\), in eV, is closest to:
- Three positive and two negative charges each of magnitude \(q\) are placed at five of the six vertices of a regular hexagon of side \(R\). The work done to bring a negative charge \(-q\) from infinity to the centre of the hexagon is:
- Consider a metal cylinder of heat capacity \(C\), thermal conductivity \(K\), mass \(m\) and radius \(r\). The combination that will have the dimension of time is:
- Let \(\theta \neq \dfrac{(2n+1)\pi}{2}\), for \(n\in\mathbb{Z}\). Consider the system of equations \[ x\cos\theta+y\sec\theta=0 \] \[ x\sin\theta+y\tan\theta=0 \] This system does not have a unique solution if and only if \(\theta\) belongs to:
View More Questions