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.
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.
Asked in UPSC NDA 1 2015 · Topic: Motion under Gravity (Variation of 'g' with altitude and depth)
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Answer: A. Both the statements are individually true and Statement II is the correct explanation of Statement I
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