Question

In the picture below, the object floats in water (density 1000 kg/m³) with one third of its volume being submerged.

The density of the object is:

		0.33 g/cm3
		0.67 g/cm3
		1.0 g/cm3
		1.33 g/cm3
		1.67 g/cm3

Answer 1

Using Force balance on object in vertical direction:

Fy_net = 0

F_b - F_a - W = 0

F_a = Force applied on object = 0, since object is floating

F_b = Buoyancy Force in upward direction = rho_w*V1*g

W = Weight of object in downward direction = m*g = rho_o*V*g

So,

Fb - W = 0

Fb = W

rho_w*V1*g = rho_o*V*g

V = Volume of object

V1 = Volume of object which is submerged = V/3

rho_w = density of water = 1000 kg/m^3 = 1 g/cm^3

So,

rho_o = density of object = rho_w*(V1/V)

rho_o = 1*((V/3)/V) = 1/3 g/cm^3

rho_o = 0.33 g/cm^3

Correct option is A.

Let me know if you've any query.