Question

A wooden cylinder floats in water , with 35% of its volume above
water. What is the density of the wooden block in S.I. system ?

Answer 1

Here,

the buoyant force exerted by water = weight of the wooden block

or

F_B = W

here

F_B = ρ_wgV_w

here is the 'ρ_w' density of water and V is the volume of water displaced. So, as 65% of wooden block is immersed

V_w = 0.65 x volume of wooden block = 0.65V

so,

F_B = ρ_wg(0.65V).........................(1)

and

W = mg = ρgV.............................(2)

here 'ρ' is the density of wood and V is the total volume of wooden block.

thus, by equating (1) and (2), we get

ρ_wg(0.65V) = ρgV

ρ_w0.65 = ρ

here ρ_w = 1000 kg/m³

so,

1000 x 0.65 = ρ

thus, density of wooden block will be

ρ = 650 kg/m³