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What is the force required (in Newtons) to hold a spherical balloon stationary in water at a depth of H from the air-water iterface? The balloon is of radius 0.1 m and is filled with air.

A. $$\frac{{4\pi {\text{g}}}}{3}$$

B. $$\frac{{0.01\pi {\text{gH}}}}{4}$$

C. $$\frac{{0.01\pi {\text{gH}}}}{8}$$

D. $$\frac{{0.04\pi {\text{gH}}}}{3}$$

This Question Belongs to Chemical Engineering >> Fluid Mechanics

1. The force required = Buoyancy force - gravitational force
Buoyancy force = mass of fluid displaced x g
mass of fluid displaced = density of fluid x volume of the balloon = 1000 x 4/3 x pi x (r^3) = 4/3 pi
Buoyancy force = 4/3 x pi x g
Gravitational force = mass of the balloon x g
mass of the balloon = density of air x volume = 1.225 x 4/3 x pi x (r^3) = 0.001225 x 4/3 pi
Gravitational force = 0.001225 x 4/3 x pi x g
The force required = Buoyancy - gravitational = 4/3 x pi x g (1 - 0.001225) = 4/3 x pi x g x 0.998 = 4/3 x pi x g

2. Pls explain

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