Question

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

1. Find:
   1. The weight of each sphere, and
   2. The upthrust on each sphere.
2. Which sphere will float? Give reason.

Answer 1

Volume of sphere A & B = 100 cm³

Density of water = 1 gcm^-3

Density of sphere A = 0.3 gcm^-3

Density of sphere B = 8.9 gcm^-3

(a)

(i) Weight of sphere A = (density of sphere A × volume) × g

= 0.3 × 100 × g = 30 gf

Weight of sphere B = (density of sphere B × volume × g)

= 8.9 × 100 × g = 890 gf

(ii) Upthrust on sphere A = Volume of sphere A × density of water × g

= 100 × 1 × g = 100 gf

Upthrust on sphere B = Volume of sphere B × density of water × g

= 100 × 1 × g = 100 gf

Since the volume of both spheres is the same inside water, the upthrust acting on them will also be same. 

(b) The sphere A will float because the density of wood is less than the density of water.