The correct option is **C. I, II, and III only**. ### Detailed Explanation: To understand why the weight of an object varies on the Earth's surface, we need to analyze each statement and how it relates to the concept of weight. 1. **Weight and Gravity**: - Weight is the force exerted by gravity on an object. It is calculated using the formula: \[ W = mg \] where \( W \) is weight, \( m \) is mass, and \( g \) is the acceleration due to gravity. The value of \( g \) can vary depending on several factors. 2. **Statement I: The Earth is not spherical but elliptical in shape**: - The Earth is an oblate spheroid, meaning it is slightly flattened at the poles and bulging at the equator. This shape affects the gravitational pull experienced at different latitudes. The gravitational force is slightly weaker at the equator compared to the poles due to the increased distance from the center of the Earth. Therefore, this statement contributes to the variation in weight. 3. **Statement II: Variation in latitude and longitude**: - Latitude affects the weight of an object because of the Earth's rotation and its shape. As mentioned, the gravitational force is stronger at the poles and weaker at the equator. Longitude does not affect weight directly, but latitude does. Thus, this statement is relevant to the variation in weight. 4. **Statement III: Rotation of the Earth on its axis**: - The rotation of the Earth causes a centrifugal force that acts outward, which reduces the effective weight of objects at the equator. This effect is negligible at the poles. Therefore, the rotation of the Earth contributes to the variation in weight experienced by objects on its surface. 5. **Statement IV: Variation in the density of the Earth**: - While the density of the Earth does vary, it does not directly affect the weight of an object on the surface in the same way that the other factors do. The density variations can influence gravitational acceleration slightly, but they are not a primary reason for weight variation on the surface. Thus, this statement is less relevant compared to the others. ### Why Other Options Are Incorrect: - **Option A: I, II, III, and IV**: - This option includes Statement IV, which, as explained, does not significantly contribute to the variation in weight on the Earth's surface compared to the other three statements. - **Option B: III and IV only**: - This option omits Statements I and II, which are crucial for understanding how the shape of the Earth and latitude affect weight. It incorrectly suggests that only the rotation and density are responsible for weight variation. - **Option D: I and II only**: - This option excludes Statement III, which is essential because the Earth's rotation significantly impacts weight due to the centrifugal force. Therefore, it does not provide a complete picture of the factors affecting weight. ### Summary: - Weight varies on the Earth's surface due to the Earth's elliptical shape, which affects gravitational pull. - Latitude influences weight, with variations in gravity experienced at different latitudes. - The Earth's rotation creates a centrifugal force that reduces effective weight, especially at the equator. - Density variations are less significant in explaining weight differences compared to the other factors. ### Revision Summary: - Weight is influenced by gravity, which varies due to the Earth's shape and rotation. - The Earth is an oblate spheroid, affecting gravitational strength at different latitudes. - The rotation of the Earth reduces effective weight due to centrifugal force. - Density variations are less impactful on weight compared to shape and rotation.