Question

5. 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' 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.​

Answer 1

(i) We know,

Weight = mg

or, $\boxed{W = \rho g V }$

For weight of the sphere made up of Iron:-

Density = 8.9 g/cm³ or 8900 kg/m³

Volume = 100 cm³ or 0.0001 m³

Take g = 10 m/s²

∴ W = (8900 kg/m³)(10 m/s²)(0.0001 m³)

⇒ W = 89 × 1 kg m/s²

⇒ W = 89 N

For weight of the sphere made up of wood:-

Density = 1 g/cm³ or 1000 kg/m³

Volume = 0.0001 m³

g = 10 m/s²

∴ W = (10 m/s²)(1000 kg/m³)(0.0001 m³)

⇒ W = 1 kg m/s²

⇒ W = 1 N

(ii) Taking water as the reference, the sphere made up of wood will float. This is because it has a smaller density than water.