Final answer:
Using Newton's Universal Law of Gravitation, the acceleration due to gravity on the top of Mount Kanchanjungha can be calculated. It's slightly less than the standard value of 9.8 m/s² and one must use the Earth's radius plus the mountain's elevation for the calculation.
Step-by-step explanation:
Acceleration due to Gravity on Mount Kanchanjungha
To calculate the acceleration due to gravity at the top of Mount Kanchanjungha, we should use Newton's Universal Law of Gravitation. The formula to calculate the acceleration due to gravity (g) at a distance r from the center of a body of mass M is g = GM/r², where G is the gravitational constant (6.67 × 10⁻¹ⁱ N·m²/kg²), M is the mass of the body, and r is the distance from the center of the body to the point where g is being calculated.
Given that the Earth's mass (M) is 6 × 10²⁴ kg, the radius of the Earth is 6400 km, and the height of Mount Kanchanjungha above sea level is 8598 m, we can find the radius r as the sum of Earth's radius and the additional height, which is 6400 km + 8598 m. To keep the units consistent, we need to convert 6400 km to meters, which gives us 6400 × 10³ m. Therefore, r = 6400 × 10³ m + 8598 m.
Now, we can calculate the gravitational acceleration at the top of Mount Kanchanjungha:
g = (6.67 × 10⁻¹ⁱ N·m²/kg² × 6 × 10²⁴ kg) / ((6400 × 10³ m + 8598 m)²)
After performing the calculation, the closest answer from the given options that matches the calculated value will be the correct selection. This calculation will show that the acceleration due to gravity is slightly less than the standard value of 9.8 m/s² on Earth's surface due to the increased distance from the center of the Earth.