The specific gravity of honey is 1.43. A cylindrical container of honey 10 feet [ft] deep is inside a dome pressurized to a surface pressure of 0.06 atmospheres [atm] on the surface of pluto. The total pressure at the bottom of the container is 67 millimeters of mercury [mm hg]. What is the gravitational acceleration of pluto, in units of meters per second squared [ m/s2]?

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aristocles aristocles · Answer 1 · 2018-10-03T03:51:06+02:00

Pressure at the bottom is given as

[tex]P = P_o + \rho* g* h[/tex]

here we know that

total pressure at the bottom is

[tex]P = 67 mm Hg[/tex]

[tex]P = 0.067* 9.8 * 13700[/tex]

[tex]P = 8995.4 Pa[/tex]

also given that

[tex]P_o = 0.06 atm = 0.06 * 1.01* 10^5 = 6060 Pa[/tex]

also the density of honey will be

[tex]\rho = 1.43 * 10^3 [/tex]

also the height is given as

h = 10 feet = 10 * 0.3048 = 3.048 m[/tex]

now from above formula

[tex]8995.4 = 6060 + 1430* g* 3.048[/tex]

[tex]8995.4 - 6060 = 4358.64* g[/tex]

[tex]g = 0.67 m/s^2[/tex]

so acceleration due to gravity on surface of pluto will be 0.67 m/s^2