Question

The variation of acceleration due to gravity $g$ with distance $d$ from the center of the earth is best represented by ($R=$ Earth’s radius):

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The correct option is D

Explanation for Correct Option:

Option (D):

From this diagram as $g$as earth's surface, distance as $R$ and $d$as depth

For the earth's surface inside as

$$\begin{gathered} g=\frac{GM}{R^3}r \\ g\alpha r \end{gathered}$$

For the earth's outside as

$$\begin{gathered} g=\frac{GM}{r^2} \\ g\alpha \frac{1}{r^2} \end{gathered}$$

So the earth's surface $g$ increases linearly with distance $R$ as shown in option $d$

Explanation for incorrect option:

a)

1. Acceleration due to gravity as continues to be at its greatest at the surface of the Earth as depth $d$ increases.
2. The aforementioned equation looks like a straight line.
3. Option a is incorrect

b)

1. As the height above the Earth's surface rises, the acceleration caused by gravity continues to decrease.
2. Option b is incorrect

c)

1. When measured inside the earth's surface, the acceleration caused by gravity will differ from the acceleration caused by gravity at the earth's surface and from the acceleration caused by gravity above the earth's surface.
2. Option c is incorrect

Hence the correct answer is option d.