1.

EXAMPLE 1.8A cube of wood floating in water supportsa 300 g mass at the centre of its top face.When the mass is removed, the cube risesby 3 cm. Determine the volume of thecube.

Answer»

Let the side of the cube be ‘a’ cm and its mass be ‘m’.

So, density of the cube is, ρ = m/a^3

Let ‘h’ be the immersed height of the cube.

So, volume immersed = ha^2

And, mass of water displaced = (ρw)ha^2

For floatation, weight of water displaced = weight of cube

=> (ρw)ha^2g = mg

=> m = (ρw)ha^2

Again, when 300 g is added to the cube the cube is immersed further by 3 cm.

So, the new volume of water displaced = (h+2)a^2

The new mass of water displaced = (ρw)(h+2)a^2

Thus,

(ρw)(h+3)a^2g = (m+300)g

=> (ρw)(h+3)a^2= (ρw)ha^2+300

For water. ρw= 1 g/cm3

So,

(h+3)a^2= ha^2+ 300

=> ha^2+ 3a2= ha^2+ 300

=> a = 10 cm

This is the length of a side of the cube.


Discussion

No Comment Found

Related InterviewSolutions