Which of these statements is true? The value of g is exactly constant at any given...

Which of these statements is true? The value of g is exactly constant at any given distance from Earth's center. The value of g is 1. The value of g changes a great deal from place to place at a given elevation on Earth's surface. The value of g is exactly constant all over Earth's surface. Even at a given distance from Earth's surface, the value of g can vary slightly.

Solutions

Expert Solution

Solution:

Let us go to the basics first.

We know that:

Following equation governs the variation of acceleration due to gravity, g with height, h:

g'/g = (1 – 2h/R)........Eqn.1 [where R = radius of earth]

So as altitude h increases, the value of acceleration due to gravity falls.

Following equation governs the variation of acceleration due to gravity, g with depth, h:

g'/g = (1 – h/R).......Eqn.2

So as depth h increases, the value of acceleration due to gravity falls.

Now coming to the question:

Which of these statements is true?

The value of g is exactly constant at any given distance from Earth's center. [FALSE]. Reason: g varies distance to distance from Earth's center as suggested by Eqn.1 above.

The value of g is 1. [FALSE]. Reason: Standard value of g is 9.8 m/s² on Earth's surface.

The value of g changes a great deal from place to place at a given elevation on Earth's surface. [FALSE]. Reason: At a given elevation, g is constant as suggested by above two equations.

The value of g is exactly constant all over Earth's surface. [TRUE]. Reason: At the Earth's surface, h = 0, so g = constant = 9.8 m/s²

Even at a given distance from Earth's surface, the value of g can vary slightly. [FALSE]. Reason: At a given distance from Earth's surface, value of g is constant and changes are negligible in its value.

Thanks!!!

genius_generous answered 2 years ago

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