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The value of g at the surface of earth is 9.8 m/s². Then the value of g′ at a place 480 km above the surface of the earth will nearly be (radius of the earth is 6400 km)

A 9.8 m/s²
B 7.2 m/s²
C 8.5 m/s²
D 4.2 m/s²

User Dhj
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1 Answer

5 votes

Final answer:

The acceleration due to gravity (g') at 480 km above Earth's surface is approximately 8.5 m/s², which is calculated using the formula for gravitational acceleration with height taken into account. The closest given answer choice is C: 8.5 m/s².

Step-by-step explanation:

The student asked what the value of g' (acceleration due to gravity) would be at a place 480 km above the surface of Earth. To calculate this, we need to modify the formula for gravitational acceleration, which is g' = GM/(R+h)^2, where G is the gravitational constant, M is the mass of the Earth, R is the radius of the Earth, and h is the height above the Earth's surface.

Given that the acceleration due to gravity at the Earth's surface (g) is 9.8 m/s² and the radius of Earth (R) is 6400 km, we plug these values into the formula to find the new value of g' at 480 km above Earth's surface:

g' = (9.8 m/s²) * (6400 km / (6400 km + 480 km))^2
= (9.8 m/s²) * (6400 / 6880)^2
= (9.8 m/s²) * (0.9302)^2
= (9.8 m/s²) * 0.8653
= 8.48 m/s²

The closest option is C: 8.5 m/s², which is approximately the value of g' at 480 km above Earth's surface. Therefore, the mentioned correct option in the final answer is C: 8.5 m/s².

User BlueWanderer
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