One goes from the centre of the earth to a distance two third the radius of the earth. The acceleration due to gravity is highest at

Options

A. the centre of the earth
B. a distance half the radius of the earth
C. a distance one-third of the radius of the earth
D. a distance two-third of the radius of the earth

Answer

To solve the question regarding the acceleration due to gravity at different distances from the center of the Earth, let's break it down step by step.

### Step 1: Understanding the Concept of Gravity Inside the Earth
- The acceleration due to gravity (g) varies depending on the distance from the center of the Earth. At the center of the Earth, g = 0 m/s². As one moves towards the surface from the center, g increases until it reaches its maximum value at the surface.

**Hint:** Remember that gravity is zero at the center of the Earth and increases as you move towards the surface.

### Step 2: Analyzing the Given Distance
- The question states that we are moving to a distance of two-thirds (2/3) of the radius of the Earth (R). This means we are at a distance of (2/3)R from the center of the Earth.

**Hint:** Visualize the Earth as a sphere and mark the center, surface, and the point at (2/3)R.

### Step 3: Comparing Distances
- To determine where the acceleration due to gravity is highest, we need to compare the distance (2/3)R with other significant points:
- At the center (0R), g = 0.
- At half the radius (1/2)R, g is greater than 0 but less than at the surface.
- At the surface (1R), g is maximum (approximately 9.8 m/s²).

**Hint:** Recall that g increases as you move from the center towards the surface.

### Step 4: Determining the Maximum Gravity
- Since (2/3)R is greater than (1/2)R but less than R, we can conclude that the acceleration due to gravity at (2/3)R is greater than at (1/2)R but less than at the surface (R).

**Hint:** Use the relationship that g increases as you approach the surface of the Earth.

### Step 5: Conclusion
- Therefore, the acceleration due to gravity is highest at the surface of the Earth (1R). However, since the question asks about the distance (2/3)R specifically, we can conclude that the acceleration due to gravity is highest at (2/3)R compared to any point below it (like (1/2)R).

**Final Answer:** The acceleration due to gravity is highest at a distance of (2/3)R from the center of the Earth.