Question

The ratio of the relative strengths of weak nuclear force and gravitational force is

• A. $10^{39}:1$
• B. $10^{13}:1$
• C. $10^{11}:1$
• D. $10^{26}:1$

Hint:

While exact values depend on the separation distance and particles involved (protons/electrons), the standard orders of magnitude usually taught are: Strong ($1$) : EM ($10^{-2}$) : Weak ($10^{-13}$) : Gravity ($10^{-39}$). Remembering this sequence helps solve such ratio problems quickly.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
There are four fundamental forces in nature. Listed in ascending order of their relative strengths (taking the Strong Nuclear Force as unity, $1$), they are:

• Gravitational Force ($F_g$): $\approx 10^{-39}$
• Weak Nuclear Force ($F_w$): $\approx 10^{-13}$
• Electromagnetic Force ($F_e$): $\approx 10^{-2}$
• Strong Nuclear Force ($F_s$): $1$

Step 2: Calculating the Ratio:
We need to find the ratio of the strength of the Weak Nuclear Force to the Gravitational Force: \[ \text{Ratio} = \frac{F_w}{F_g} \] Substituting the approximate standard values: \[ \text{Ratio} \approx \frac{10^{-13}}{10^{-39}} \] Using the laws of exponents ($\frac{a^m}{a^n} = a^{m-n}$): \[ \text{Ratio} = 10^{-13 - (-39)} = 10^{-13 + 39} = 10^{26} \]
Step 3: Final Answer:
The ratio is $10^{26}:1$, which corresponds to Option (D).