Statement-I: A body weighs less on a hill top than on earth’s surface

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

Both the statements are individually true and Statement II is the correct explanation of Statement I
Both the statements are individually true but Statement II is not the correct explanation of Statement I
Statement I is true but Statement II is false
Statement I is false but Statement II is true
This question was previously asked in
UPSC NDA-1 – 2015
The correct option is A. Both statements are individually true, and Statement II is the correct explanation of Statement I.
Statement I is true because weight (W) is defined as mass (m) multiplied by the acceleration due to gravity (g), W = mg. A body’s mass remains constant regardless of location.
Statement II is true because the acceleration due to gravity (g) decreases with increasing height above the Earth’s surface. The gravitational force, and hence ‘g’, depends on the distance from the center of the Earth. At a higher altitude like a hill top, this distance is greater than on the surface at sea level. The relationship is approximately g’ = g(R/(R+h))², where R is Earth’s radius and h is height. As h increases, g’ decreases.
Since weight is directly proportional to ‘g’ (with constant mass), a decrease in ‘g’ at a hill top compared to the Earth’s surface directly causes the body to weigh less. Therefore, Statement II provides the correct reason for Statement I.