Question

How can the experimental value of acceleration due to gravity be calculated?

1) Using the formula g = 2π/T²
2) Using the formula g = 4π²R/T²
3) Using the formula g = 2π²R/T²
4) Using the formula g = 4π²/T²

Answer 1

The experimental value of acceleration due to gravity can be calculated using the formula g = 4π²R/T².

So. the correct option is 2.

Step-by-step explanation:

To calculate the experimental value of acceleration due to gravity one can use the formula g = 4π²R/T². In this formula g represents the acceleration due to gravity R is the radius of the orbit and T is the period of revolution.

This formula is derived from Keplers third law which relates the period of revolution of a celestial body to its average distance from the center of mass.The formula g = 4π²R/T² specifically applies to objects in orbit such as satellites around a celestial body.

By measuring the period of revolution and the radius of the orbit for a satellite researchers can use this formula to determine the acceleration due to gravity at that location.

It provides a practical and direct method for experimental determination offering a valuable tool in the field of celestial mechanics. Keplers third law and its application in determining the orbital dynamics of celestial bodies.

So. the correct option is 2.

Answer 2

The experimental value of acceleration due to gravity (g) can be calculated using the formula g = 4π²R/T².Thus,the correct option is d.

Step-by-step explanation:

The formula for calculating the acceleration due to gravity is derived from the equation for the period of a simple pendulum. In this case, the correct formula is g = 4π²R/T², where 'g' is the acceleration due to gravity, 'R' is the length of the pendulum, and 'T' is the period of the pendulum.

The formula is derived from the relationship between the period of a simple pendulum and the acceleration due to gravity. The period (T) is the time it takes for one complete oscillation of the pendulum, and it is related to the length of the pendulum (R) and the gravitational acceleration (g) through the formula T = 2π√(R/g). By rearranging this formula, we get the expression for gravity as g = 4π²R/T².

This formula is commonly used in experimental setups where the period of a pendulum is measured, and the length of the pendulum is known. By substituting these values into the formula, the experimental value of gravity can be determined. It's crucial to note that the correct formula includes the factor of 4 in the numerator, distinguishing it from other similar-looking equations.

Therefore,the correct option is d.