Question

Earth is assumed to be a sphere of radius \( R \) and uniform density. The variation of acceleration due to gravity (g) according to the depth and the height (h) from the Earth's surface is shown correctly by the graph

• (C)
• (B)
• (D)
• (A)

Hint:

Gravity decreases linearly with depth inside the Earth and decreases with the square of the distance from the Earth's center as height increases.

Answer 1

The Correct Option is A

Step 1: Gravity at depth and height.
The acceleration due to gravity at a depth \( h \) below the Earth's surface decreases linearly with depth, and it is given by the equation: \[ g_{\text{depth}} = g_{\text{surface}} \left( 1 - \frac{h}{R} \right) \] where \( R \) is the Earth's radius, and \( g_{\text{surface}} \) is the gravitational acceleration at the Earth's surface. At a height \( h \) above the Earth's surface, the acceleration due to gravity decreases as: \[ g_{\text{height}} = g_{\text{surface}} \left( \frac{R}{R + h} \right)^2 \] Step 2: Graph analysis.
Option (C) correctly shows the graph where gravity increases linearly with depth and decreases with height. Other options do not match this physical behavior.
Step 3: Conclusion.
Thus, the correct answer is (C).