Question

Using Figures A and B, find the volume of the object submerged in the water and its density. (Assume Wapp 0.2 N and Wo0.N. Enter your answers to at least three significant figures.) Wapp Figure A Fiure B Vo = 1.02E-5 g/cm3

Answer 1

Given,

Weight of the object, W₀ = 0.3 N

Apparent weight, W_app = 0.2 N

Now,

Let mass of the object be m

As we know,

W₀ = mass * acceleration due to gravity

=> W₀ = m*g

=> 0.3 = m * 9.8

=> m = 0.3 / 9.8 = 0.0306122 kg = 30.6122 gm

Now,

density of water, $\rho$ _water = 1000 kg/m³

Let volume of the object be V

Apparant weight, W_app = W₀ - weight of the liquid displaced

                                      = W₀ - $\rho$ _water*V*g

=> W_app = W₀ - $\rho$ _water*V*g

=> 0.2 = 0.3 - ( 1000 * V * 9.8 )

=> 9800 * V = 0.1

=> V = 0.1 / 9800 = 1.02041 * 10^-5 m³

Now, 1 m³ = 10⁶ cm³

Thus,

V = 1.02041 * 10^-5 * 10⁶ cm³

=> V = 10.2041 cm³

Now,

We have mass of the object, m = 30.6122 gm

Volume, V = 10.2041 cm³

Now,

density, $\rho$ _object = mass / Volume = 30.6122 / 10.2041

=> $\rho$ _object =2.999 g/cm³

density of the object is 2.999 g/cm³