Statement I : A body weighs less on a hill top than on earth’s surface even though its mass remains unchanged. Statement I : The acceleration due to gravity of the earth decreases with height.

Statement I is true because weight is the gravitational force exerted by the Earth on an object, which is calculated as the product of mass and acceleration due to gravity (W = mg) [2]. While mass remains constant regardless of location, weight varies with changes in gravitational acceleration [1]. Statement II is also true and provides the correct explanation for Statement I. The acceleration due to gravity (g) is inversely proportional to the square of the distance from the Earth's center [2]. As an object moves to a hilltop (increasing height 'h'), the distance from the center (R + h) increases, causing the value of 'g' to decrease. Since weight depends directly on 'g', a body weighs less at higher altitudes like hilltops compared to the Earth's surface [2].

Sources

1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > A step further > p. 75
2. [2] https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/weight-equation/