**Answer:**

**Introduction:**
The acceleration due to gravity is the force that attracts objects towards the center of the Earth. It is denoted by the symbol 'g' and has a value of approximately 9.8 m/s^2 near the surface of the Earth. The acceleration due to gravity varies with height and depth from the surface of the Earth. In this question, we are given that the acceleration due to gravity at a height of 1 km above the Earth is the same as at a depth 'd' below the surface of the Earth. We need to find the value of 'd' based on this information.

**Understanding the problem:**
To solve this problem, we need to compare the gravitational acceleration at a height of 1 km above the Earth's surface with the gravitational acceleration at a depth 'd' below the Earth's surface. We know that the gravitational acceleration decreases with increasing height and increases with increasing depth. We need to find the value of 'd' where the gravitational acceleration is the same as at a height of 1 km above the Earth's surface.

**Analysis:**
Let's consider the gravitational acceleration at a height of 1 km above the Earth's surface as 'g1' and the gravitational acceleration at a depth 'd' below the Earth's surface as 'g2'. We know that the gravitational acceleration at a height 'h' above the Earth's surface is given by the formula:

g1 = g * (R / (R + h))^2

where R is the radius of the Earth and g is the acceleration due to gravity at the Earth's surface.

Similarly, the gravitational acceleration at a depth 'd' below the Earth's surface is given by the formula:

g2 = g * (R / (R - d))^2

**Comparison of g1 and g2:**
We are given that g1 = g2. Substituting the expressions for g1 and g2, we get:

g * (R / (R + 1))^2 = g * (R / (R - d))^2

Simplifying the equation, we get:

(R / (R + 1))^2 = (R / (R - d))^2

Taking the square root on both sides and simplifying further, we get:

(R / (R + 1)) = (R / (R - d))

Cross-multiplying the equation, we get:

R - d = R + 1

Simplifying further, we get:

d = 1

**Conclusion:**
From the above analysis, we can conclude that the value of 'd' is 1 km. Therefore, option (1) d=1Km is the correct answer.

The correct answer is option number 3rd that is d=2km !

explanation : Acceteration due to gravity at height h, 
gn​=g0​(1−R2h​)  h=1km
Acceleration due to gravity at depth d,
dd​=g0​(1−Rd​)
gh​=gd​
g0​(1−R2h​)=g0​(1−Rd​)
→d=2h
=2×1km
d=2km