Question

The gravitational force exerted on a solid object is 6.0 N. When the object is suspended from a spring scale and immersed in water, the reading on the scale is 3.00 N. Find the density of the object.

Answer 1

Given

gravitational force exerted on a solid object is F = mg = 6 N ===> mass of the object is m = F/g = 6/9.8 kg = 0.612245 kg

when the object is immersed in water the scale shows 3 N only (force)

that is the buoyance force will be exerted by water on the object = 6-3 = 3 N

we know that the buoyance force Fb = rho*v*g = 3 N

here v is the volume of the displaced water and rho is density of water , g acceleration due to gravity

that is 1000 *V*9.8 = 3 ==> displaced volume of water = 0.000306122 m^3 = 3.0612*10^-4 m^3 = volume of the object when it is immersed in water

So the density of the object is density = mass/volume

density = 0.612245 kg /3.0612*10^-4 m^3 = 2000.016 kg /m^3 = 2000 kg /m^3

the density of the solid object is 2000 kg/m^3