(a) Derive an expression for the buoyant force on a spherical balloon, submerged in water, as a function of the depth h below the surface, the volume Vi of the balloon at the surface, the pressure P0 at the surface, and the density rw of the water. Assume the water temperature does not change with depth. (b) Does the buoyant force increase or decrease as the balloon is submerged?
(c) At what depth is the buoyant force onehalf the surface value?

yup its correct its: c) b b

grav force prop 1/r squared 2r all squared is 4rsquared 1/4rsquared quartered

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.