Question

A block 3cm by 4cm is partially immersed to a depth of 6cm in a pail of water. a) What is the density of the block? b) What weight of metal is placed atop the block will fully submerge it?

Answer 1

Assume that the height of the block is 9 cm.

(a)

$mg=\rho gV\to \rho_0V_0g=\rho gV\to\rho_0=\frac{\rho V}{V_0}=$

$=\frac{1000\cdot0.03\cdot0.04\cdot0.06}{0.03\cdot0.04\cdot0.09}\approx667(kg/m^3)$

(b)

$(W+mg)=\rho g V\to W=\rho g V-mg=$

$=1000\cdot9.81\cdot0.03\cdot0.04\cdot0.09-667\cdot0.03\cdot0.04\cdot0.09\cdot9.81=0.35(N)$