Question

what is the density of a block of wood that floats in water with 0.1 of its volume above water.

Answer 1

0.1=>1/10

let whole volume be 1

So,
1-1/10=>10-1/10=>9/10


V=9/10

Vdg=Vdg
Comparing both side we get
Vd=Vd
L.H.S. be block of wood and R.H.S be water

1×1=9/10×d
1=9/10d
10/9=d
or
1.12g/cm³=d

Answer 2

Dear Student,

◆ Answer -

Density of wooden block = 1111 kg/m^3

● Explanation-

Let V0 be volume of the wooden block and V be that for immersed part.

For an wooden block to float-

Buoyanct force by immersed wooden block = Weight of wooden block

d.V.g = d0.V0.g

V = d0.V0/d

Volume of wooden block outside water-

V' = V0 - V

V' = V0 - V0.d0/d

V' = V0 (1-d0/d)

Fraction of outside part to total volume-

V' / V0 = V0(1-d0/d) / V0

V' / V0 = 1 - d0/d

Given that V' = 0.1 V0

0.1V0 / V0 = 1 - 1/d

1/d = 1 - 0.1

d = 1/0.9

d = 1.111 g/cm^3

d = 1111 kg/m^3

Hence, density of wooden block is 1111 kg/m^3.

Hope that is helpful...