Question

Find the ratio of the magnitude of the electric force to the gravitational force acting between two protons

• A. ${10}^{30}$
• B. ${10}^{32}$
• C. ${10}^{34}$
• D. ${10}^{36}$

Answer 1

The correct option is D ${10}^{36}$

We know, Charge on one Proton = + 1.6 × 10⁻¹⁹ C.and Mass of the Proton = 1.6727 × 10⁻²⁷ kg.

Now, Using the Coulomb's Law,

F = (k q₁ q₂) ÷ r²

where,

k = 8.99 × 10⁹ Nm²kg⁻²

k ≈ 9 × 10⁹ Nm²kg⁻²

q₁ = q₂ = 1.6 × 10⁻¹⁹ C

r = Distance between the Two Protons.

Now,

F = 9 × 10⁹ × (1.6 × 10⁻¹⁹)² ÷ r²

⇒ F₁ = 23.04 × 10⁻²⁹/r² -----eq(i)

Now, Using Newton's law of Gravitation,

Here, G = Gravitation Constant whose value is 6.67 × 10⁻¹¹ Nm²kg⁻².

⇒ F r² = 6.67 × 10⁻¹¹ × (1.6727 × 10⁻²⁷)²

⇒ F₂ = 18.66 × 10⁻⁶⁵/r²

Now, Let us calculate the ratio of the Electrostatic Forces to the Gravitational Force between the Two Protons.

∴ F₁/F₂ = (23.04 × 10⁻²⁹/r²) ÷ (18.66 × 10⁻⁶⁵/r²)

⇒ F₁/F₂ = 1.24 × 10³⁶

Hence,

Option $\left(D\right)$ is correct answer.