मराठी
Maharashtra State BoardHSC Science (General) 11th Standard
पाठ्यपुस्तक उत्तरे९०७७
संकल्पना स्पष्टीकरण आणि व्हिडिओ४७६
अभ्यासक्रम

Variation in the Acceleration>Effect of the shape of the Earth

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Topics

  • Introduction
  • Definition: Weight of an Object
  • Formula: Weight of an Object
  • Characteristics
  • Understanding Fravity Variation
  • Significance
  • Ral-Life Examples
Maharashtra State Board: Class 11

Introduction

The Earth's shape is often assumed to be a sphere, but it is actually an ellipsoid. This means the Earth is slightly bulged at the equator. This non-spherical shape, combined with the Earth's rotation, causes the acceleration due to gravity (g) to vary across the planet. This variation in g directly influences the weight of objects at different locations.

Maharashtra State Board: Class 11

Definition: Weight of an object

"Weight of an object is the force with which the Earth attracts that object."

Maharashtra State Board: Class 11

Formula: Weight of an object

w = mg
where: 
  • w is the weight of the object.
  • m is the mass of the object.
  • g is the acceleration due to gravity.
Maharashtra State Board: Class 11

Characteristics

  • The Earth is an ellipsoid, not a perfect sphere.
  • The Earth is bulged at the equator.
  • Equatorial radius (6378 km) is greater than the polar radius (6356 km).
  • Acceleration due to gravity is minimum at the equator (gE = 9.7804 m/s2).
  • Acceleration due to gravity is maximum at the poles (g = 9.8322 m/s2).
Maharashtra State Board: Class 11

Understanding Gravity Variation

The variation in the acceleration due to gravity (g) is due to the combined effect of two factors at the equator:

  1. Greater Radius: Since the equator is bulged, objects on the equator are farther from the Earth's center compared to objects at the poles. The greater the distance (radius), the less the gravitational force.
  2. Rotation: The Earth's rotation also reduces the effective gravitational force at the equator.

As a result of these two effects, the value of g is smallest at the equator (9.7804 m/s2) and largest at the poles (9.8322 m/s2).

The weight (w) of an object is calculated as w = mg. Since the value of g changes with latitude (equator to pole), weight also changes. The weight of an object is minimum at the equator because g is minimum there.

The value of g (and thus the weight) also changes with:

  • Altitude: Weight reduces with increasing height above the Earth’s surface.
  • Depth: Weight reduces with increasing depth below the Earth’s surface.
Maharashtra State Board: Class 11

Significance

  • The true shape of the Earth (ellipsoid) results in non-uniform gravity across its surface.
  • The difference in g values between the equator and poles (9.7804 m/s2 vs. 9.8322 m/s2) is measurable.
  • It demonstrates that an object's weight is not constant but depends on its location relative to Earth's center and its motion.
Maharashtra State Board: Class 11

Real-Life Examples

  • Space Launches: Launching near the equator saves fuel due to lower gravity and Earth’s spin boost.
  • Precision Measurements: Gravity varies by location, so it must be considered in accurate scientific experiments.
 

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