The gravitational force exerted on a solid object is 5.13 N. When the object is suspended from a spring scale

The gravitational force exerted on a solid object is 5.13 N. When the object is suspended from a spring scale and submerged in water, the scale reads 3.94 N. Find the density of the object.

if the weight is 5.13N, its mass is 5.13N/9.8m/s/s = 0.52kg

the water exerts a buoyant force of 5.13-3.94 = 1.19N on the mass, meaning 1.19N of water were displaced; we now find how much volume of water was displaced

this means that the displaced water has a weight of rho(water) V g and this equals 1.19N, therefore

1000kg/m^3 x V x 9.8m/s/s = 1.19N

V = 1.2x10^-4m^3 is the volume of displaced water

since the object was submerged this is also the volume of the object, therefore, its density is

density = mass/volume = 0.52kg/1.2x10^-4m^3 = 4333kg/m^3

That means the buoyancy force of the water is 5.13–3.94 = 1.19 N
The density of water, 998 kg/m³, which translates to 998x9.8 = 9780 N/m³
1.19 N / 9780 N/m³ = 0.0001217 m³ which is the volume of the object

The mass is 5.13 / 9.8 = 0.523 kg
Density = 0.523 kg / 0.0001217 m³ = 4301 kg/m³