### Exploring Pressure, Force, and Gravity on a Distant World#### Background InformationConsider a distant world that has a surface gravity of \(5.92 \, \text{m/s}^2\) and an atmospheric pressure of \(7.24 \times 10^4 \, \text{Pa}\) at its surface.### Problem Set#### (a) Force Exerted by the Atmosphere**Question:** What force is exerted by the atmosphere on a disk-shaped region with a radius of \(2.00 \, \text{m}\) at the surface of a methane ocean?**Solution:**To find the force, we use the formula \( F = P \times A \), where \( F \) is the force, \( P \) is the pressure, and \( A \) is the area of the disk-shaped region.1. Calculate the area \( A \) of the disk: \[ A = \pi r^2 = \pi (2.00 \, \text{m})^2 = 4\pi \, \text{m}^2 \]2. Compute the force: \[ F = 7.24 \times 10^4 \, \text{Pa} \times 4\pi \, \text{m}^2 = 2.90 \times 10^5 \pi \, \text{N} \]**Answer:** The force exerted by the atmosphere is \( 9.12 \times 10^5 \, \text{N} \).#### (b) Weight of Liquid Methane Column**Question:** What is the weight of a \(10.0\)-meter deep cylindrical column of methane with a radius of \(2.00 \, \text{m}\)? Note: The density of liquid methane is \(415 \, \text{kg/m}^3\).**Solution:**To find the weight, we first determine the mass of the methane column and then calculate the weight using \( W = mg \) where \( W \) is the weight, \( m \) is the mass, and \( g \) is the gravitational acceleration.1. Calculate the volume \( V \) of the cylinder: \[ V = \pi r^2 h = \pi (2.00 \, \text

a) The required force is, b) The required weight is,

Answered: Suppose a distant world with surface…

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