Question

An object of mass 1.6 kg and volume 0.0022 m3 is placed into a fluid of density 1.33 ✕ 103 kg/m3. The fluid is at rest.

(a) Will the object float or will it sink in the fluid? float sink

(b) If it floats, what fraction of volume is immersed in the fluid? If it sinks, find its acceleration, ignoring any drag force on the object. (Enter the magnitude of the acceleration if it sinks.)

Answer 1

a)
density of the object, rho = mass/volume

= 1.6/0.0022

= 727 kg/m^3

density of the object is less than density of the fluid. so, the object floats in the fluid.

b) let V is the volume of the object immersed

in the equilibrium, Net force on the object = 0

buoyant force - m*g = 0

rho_fluid*V*g - m*g = 0

rho_fluid*V*g - rho_object*V_object*g = 0

rho_fluid*V*g = rho_object*V_object*g

rho_fluid*V = rho_object*V_object

V/V_object = rho_object/rho_fluid

= 727/(1.33*10^3)

= 0.547

54.7% of the volume is immersed in the fluid.