Question

A 5.5 g jewel has an apparent weight of 28 mN when submerged in water. Show that the jewel cannot be diamond (density 3.51 g/cm³) by giving its specific gravity.

Answer 1

True Weight = 0.0055 kg x 9.8m/s^2 = 0.0539 Newtons
Do a free body diagram when jewel is under water.
Assume that the jewel is denser than water and sinks to bottom of tank creating a normal force from the bottom. Normal force is equal to its apparent weight because every force as an equal but opposite reaction.

3 forces acting on jewel.
Bouyant force, gravitational, and normal
Net Force = (Density water x volume of water displaced x9.8) + 0.028 N - 0.0539 N = 0
Net force = (1g/cm^3 x V water x 9.8) + 0.028 - 0.0539N = 0

Solve for V water = 0.00264 cm^3
Volume of water displaced is = to volume of jewel
d=m/v= 5.5g / 0.00264cm^3 = 2083.33 g/cm^3

Density of jewel is 2083.33 g/cm^3 and density of diamond is 3.51. Densities dont match. so jewel cannot be diamond