Statement I: The acceleration due to gravity decreases with increase in height from the surface of the Earth. Statement I : The acceleration due to gravity is inversely proportional to the square of the distance from the centre of the Earth.

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Q: 66 (NDA-I/2014)
Statement I: The acceleration due to gravity decreases with increase in height from the surface of the Earth.
Statement I : The acceleration due to gravity is inversely proportional to the square of the distance from the centre of the Earth.

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,28,5,28,2,2,1

keywords: 

{'gravity decreases': [0, 0, 0, 1], 'acceleration': [0, 0, 2, 8], 'gravity': [0, 0, 0, 6], 'earth': [0, 1, 1, 1], 'height': [0, 0, 1, 2], 'increase': [3, 1, 10, 35], 'square': [0, 0, 0, 1], 'distance': [0, 3, 3, 3]}

In this question, we are given two statements regarding the acceleration due to gravity and its relationship with height from the surface of the Earth.

Statement I states that the acceleration due to gravity decreases with an increase in height from the surface of the Earth. This statement is true. As an object moves higher from the surface of the Earth, it gets farther from the Earth`s center of mass, resulting in a decrease in the gravitational force acting on it. This decrease leads to a decrease in the acceleration due to gravity.

Statement II states that the acceleration due to gravity is inversely proportional to the square of the distance from the center of the Earth. This statement is also true. The formula for the gravitational acceleration (g) is given by g = GM/r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth. As the distance (r) increases, the value of r^2 in the denominator increases, leading to a decrease in the value of g. Therefore, Statement II is a correct explanation of Statement I.

Hence, option 1 is the correct answer as both statements are true and Statement II is the correct explanation of Statement I.