If the period T of a simple pendulum depends on its length L, mass m, and acceleration due to gravity g, then using dimensional analysis, the period T is proportional to ________.

Correct option is C

The correct answer is (C) $$\sqrt{\frac{L}{g}}$$​

Lg\sqrt{\frac{L}{g}}

Explanation:

• Using dimensional analysis, the period $T$ of a simple pendulum is proportional to the square root of the ratio of length (L) to gravitational acceleration (g). This is expressed as:

  ​$$T = 2\pi \sqrt{\frac{L}{g}}$$​​
  

​Thus, the period is proportional to $$\sqrt{\frac{L}{g}}$$​​

Lg\sqrt{\frac{L}{g}} ​Information Booster:

• Dimensional Analysis: This technique helps determine the relationship between physical quantities based on their dimensions. In the case of a simple pendulum, it shows that the period depends only on length and gravity, and not on mass.

• Period of a Simple Pendulum: The formula for the period of a simple pendulum is: $$T = 2\pi \sqrt{\frac{L}{g}}$$ 

  This indicates that the period is proportional to the square root of the length and inversely proportional to the square root of gravity.