Final answer:
To find the distance at which the acceleration due to gravity is one hundred times smaller than at the surface of the earth, we can use the equation for gravitational acceleration. By solving the equation, we find that the distance is 9 times the radius of the earth, which is approximately 57,204 km. Therefore, the correct answer is d) Not Mentioned.
Step-by-step explanation:
To find the distance above the surface of the earth at which the acceleration due to gravity is one hundred times smaller than at the surface, we can use the formula for gravitational acceleration:
g = G * (M / r^2)
where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the earth, and r is the distance from the center of the earth.
Let's call the distance above the surface of the earth where the acceleration is one hundred times smaller than at the surface as d. We can set up the following equation:
g / (100 * g) = (r / (r + d))^2
Simplifying the equation, we get:
1 / 100 = (r / (r + d))^2
Taking the square root of both sides, we have:
1 / 10 = (r / (r + d))
10r = r + d
9r = d
Therefore, the distance above the surface of the earth is 9 times the radius of the earth.
The radius of the earth is approximately 6,356 km, so the distance above the surface of the earth is:
9 * 6,356 km = 57,204 km
Therefore, the correct answer is d) Not Mentioned.