Calculate Gravitational Acceleration at the Bottom of Sea

What is the value of gravitational acceleration at the bottom of the sea 7 km deep?

Given data: diameter of Earth is 12800 km and g on the surface of the Earth is 9.8 m/s². [9.789 m/s²]

Answer:

The value of gravitational acceleration at the bottom of the sea 7 km deep is approximately 9.79 m/s².

Explanation: The question asks for the gravitational acceleration at the bottom of the sea, which is 7 km deep. This calculation involves understanding how the gravitational acceleration, denoted as g, changes in relation to the distance from the surface of the Earth.

When you are at the bottom of the sea, you are closer to the center of the Earth compared to being on the surface. This proximity to the Earth's center affects the value of gravitational acceleration, resulting in a decrease from the standard 9.8 m/s² experienced on the surface.

Calculating the specific value of gravitational acceleration at the bottom of the sea requires considering factors like Earth's density and mass distribution. In this scenario, we will use a simplified formula to provide an approximate answer.

The formula for calculating g' (gravitational acceleration at a certain depth) is given by g' = (1 - d/Re) * g, where d is the depth below the surface, Re is the radius of the Earth, and g is the surface gravity.

Given the values provided: g on the surface is 9.8 m/s², the Earth's radius (Re) is half of the diameter at 6400 km, and the depth (d) is 7 km, we can plug in these values to find g'.

Substitute the values into the formula: g' = (1 - 7/6400) * 9.8 ≈ 9.79 m/s²

Therefore, the value of gravitational acceleration at the bottom of the sea 7 km deep is approximately 9.79 m/s², slightly less than the value experienced on the surface.