1. Introduction:

Gravity is the force that attracts objects towards the centre of the Earth. The acceleration due to gravity (g) is the acceleration experienced by an object when it falls freely under the influence of the Earth’s gravitational force.

2. Value of Acceleration due to Gravity (g):

The standard value is at the surface of the Earth. This value can vary slightly based on altitude, latitude, and local geological conditions.

3. Formula for Acceleration due to Gravity:

Acceleration due to Gravity is derived from Newton’s Law of Universal Gravitation.

Where;

= Gravitational force,

= Universal gravitational constant (),

= Mass of the Earth,

= Mass of the object,

= Distance between the centres of the two masses.

For an object on the surface of the Earth, it can be equated to…

Simplifying gives:

Where:

= Mass of the Earth (),

= Radius of the Earth ().

4. Factors Affecting Acceleration due to Gravity:

Altitude (Height above Sea Level):

Decreases with an increase in altitude as the distance from the centre of the Earth increases.

The new value of at a height:

Depth (Below the Surface):

Decreases linearly as one goes deeper below the Earth’s surface.

ü At a depth, is given by:

Latitude:

Due to the Earth’s rotation, is slightly less at the equator than at the poles.

The centripetal force due to rotation reduces the effective gravity.

Read Also: Universal Law of Gravitation-Class 11 Physics

 5. Variation of g with Latitude:

The Earth is not a perfect sphere; it is an oblate spheroid (flattened at the poles and bulging at the equator).

The effective value of at latitude:

Where is the angular velocity of Earth’s rotation?

 6. Derivation of g from Newton's Second Law:

When an object falls freely, the only force acting on it is gravity.

By Newton’s Second Law:

Where, so:

Simplifying:

7. Practical Implications of…

Projectile Motion: The value influences the range, maximum height, and time of flight.

Free Fall: When an object falls under gravity alone, its velocity and position at any time can be found using:

8. Experimental Measurement of g.

Simple Pendulum: The time of a simple pendulum is given by:

Where is the length of the pendulum?

By measuring and, can be determined using:

9. Important Points to Remember:

Is maximum at the poles and minimum at the equator.

Does not depend on the mass of the falling object (Galileo’s experiment).

Dimensional formula of: [].

10. Practice Problems:

1. Calculate the value of a height above the Earth's surface.

2. If at the Earth's surface is, find at a depth of below the surface.

3. Using the pendulum experiment, determine when and

Conclusion:

Understanding acceleration due to gravity is crucial for grasping various physical phenomena and applications in physics. Its variations based on altitude, depth, and latitude play an essential role in calculations relevant to engineering and scientific research. Mastery of these concepts aids in solving practical problems and enhances comprehension of gravitational effects on motion.

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