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As we go below the earth surface, the gravitational acceleration _____________.
1. decreases
2. increases
3. remains constant
4. either 1 or 2

1 Answer

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Best answer
Correct Answer - Option 1 : decreases

CONCEPT:

  • Gravitational acceleration: An acceleration that an object receives due to the force of gravity acting on it.
  • Gravitational Acceleration: It is calculated by using the formula

\(g = {GM\over R^2}\)

where g is the gravitational acceleration, G is the gravitational constant, M is the mass of the earth and R is the radius of the earth.

  • When an object is at depth 'd', gravitational acceleration: It is calculated by

\(g_{_d} = g (1-{d\over R})\)

where gd is the gravitational acceleration at depth d, g is the gravitational acceleration at the surface, and R is the radius of the earth.

EXPLANATION:

Gravitational acceleration at the depth d is given by

\(g_{_d} = g (1-{d\over R})\)

As we go below the earth's surface, the depth 'd' will increase.

As d increases, \( (1-{d\over R})\) will decrease.

As \( (1-{d\over R})\) decreases, \(g (1-{d\over R})\) will also decrease.

So gd will decrease with depth.

  • So as we go below the earth's surface, the gravitational acceleration decreases.
  • Hence the correct answer is option 1.

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