# How to determine the formula if physical quantities are given

For this we should know the dependence of the physical quantity on other quantities and consider it as a product type of the dependence.

Q)Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length (l), mass of the bob (m) and acceleration due to gravity (g). Derive the expression for its time period using method of dimensions.

The dependence of time period T on the quantities l, g and m as a product may be written as

where k is dimensionless constant and x, y and z are the exponents. By considering dimensions on both sides, we have

On equating the dimensions on both sides, we have

x + y = 0; –2y = 1; and z = 0

## Most Viewed Questions

### Preparation Products

##### Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, Faculty Support.

₹ 29999/- ₹ 24999/-
##### Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
##### Knockout NEET (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports.

₹ 7999/- ₹ 4999/-
##### Knockout NEET 2023 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports.

₹ 13999/- ₹ 6999/-