Question

An empty glass test tube floats vertically in water to a depth of 5 cm. Now, on introducing a 8 cm liquid column into the tube, its depth in water is further Now the empty test tube is increased by 4 cm. N allowed to float vertically in the liquid, 5 cm of the tube is seen in air. Find the total length of the tube.

Answer 1

Let cross sectional area of tube$=A$

length of tube$=L$

for equilibrium$,$

weight of tube$W_T=$ buoyancy force by water

So$,$

$W_T=$ ${\rho }_{w}gA\times 5$

after pouring liquid$,$

$W_T={\rho }_{w}gA\times 8={\rho }_{w}gA\times 9$

${\rho }_{w}gA\cdot 5={\rho }_{w}gA\cdot 8={\rho }_{w}gA\cdot 9$

$\Rightarrow {\rho }_l=\frac{{\rho }_w}{2}.$