Question

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

Concept of Physics - 1 , HC VERMA , Chapter "The Force"

Answer 1

Hello Dear.

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,

$F = G \frac{m_{1} m_{2} }{r^{2} }$

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, the Ratio is 1.24 × 10³⁶.



Hope it helps.

Answer 2

First page Second page

Answer:

1.24 ×10^-36

Explanation:

Check both the pictures for explanation and process.