Two spheres A and B, each of volume 100 cm³ are placed on water (density = 1.0 g cm^-3). The sphere A is made of wood of density 0.3 g cm^-3 and the sphere B is made of iron of density 8.9 g cm^-3.

(a) Find (i) the weight of each sphere, and (ii) the upthrust on each sphere.

(b) Which sphere will float ? Give reason.

(a) Weight of sphere = volume of sphere x density of iron x g    [Equation 1]

Upthrust = volume of water displaced x density of water x g    [Equation 2]

Given,

Density of water = 1 g cm^-3

Density of sphere A = 0.3 g cm^-3

Density of sphere B = 8.9 g cm^-3

Volume of sphere A & B = 100 cm³

Substituting the values in the formula 1, we get weight of sphere A and B,

Weight of sphere A = 100 x 0.3 x g = 30 gf

Weight of sphere B = 100 x 8.9 x g = 890 gf

(ii) Substituting the values in the formula 2, we get upthrust on A and B,

Upthrust on sphere A = 100 x 1 x g = 100 gf

Upthrust on sphere B = 100 x 1 x g = 100 gf

(b) Sphere A will float.
The upthrust on sphere A is 100 gf which is more than its weight of 30 gf hence sphere A will float with its that much part submerged for which upthrust becomes equal to its weight of 30 gf. The upthrust on sphere B is also 100 gf but it is less than its weight of 890 gf hence sphere B will sink. In general, if the density of the body is less than the density of the liquid then it will float, and as the density of wood is lesser than the density of water hence sphere A floats.