What is the net force inward acting on a spherical bathysphere of diameter 2.00 m at an ocean depth of 1000 m? (The pressure inside the bathysphere is, hopefully, 1 ATM.) $\rho$(sea water) = 1.02 *103 kg/m3.
A)1.26 * 104 N
B)1.26 * 106 N
C)1.26 * 108 N
D)1.26* 1010 N
E)1.26 * 102 N

Question

Quizplus · Accepted Answer

The net force inward acting on the bathysphere is given by the difference between the force due to the pressure of the water outside and the pressure of the air inside. Assuming that the pressure inside the bathysphere is 1 ATM, the pressure outside is given by:
P = ρgh
where ρ is the density of seawater, g is the acceleration due to gravity, and h is the depth of the bathysphere. Substituting the given values, we get:
P = (1.02 x 10^3 kg/m^3) x (9.81 m/s^2) x (1000 m)
P = 1.00 x 10^7 Pa
The force due to this pressure acting on the surface area of the bathysphere is:
F = PA
where A is the surface area of the bathysphere. Substituting the given values, we get:
F = (1.00 x 10^7 Pa) x π(1.00 m)^2
F = 3.14 x 10^7 N
The force due to the pressure inside the bathysphere is simply the atmospheric pressure times the surface area:
F = PA = (1 ATM) x π(1.00 m)^2 = 3.14 x 10^4 N
Therefore, the net force inward acting on the bathysphere is:
Fnet = Foutside - Finside = 3.14 x 10^7 N - 3.14 x 10^4 N = 1.26 x 10^8 N or 1.26 x 10^10 dynes. 
The answer in SI units is 1.26 x 10^8 N, which corresponds to choice C.

What Is the Net Force Inward Acting on a Spherical ρ\rhoρ

What Is the Net Force Inward Acting on a Spherical $\rho$