Question

A boat floating in a tank of water is carrying passengers. If the passengers drink some of the water surrounding the boat in the tank , how will it affect the water level of the tank?

• A. It will go down
• B. It will rise
• C. It will remain unchanged
• D. It will depend on atmospheric pressure

Answer 1

The correct option is C

It will remain unchanged

Let us first consider a situation where you have a container floating in water in a tank and you add $V_2$ volume of water from outside (not from the water in the tank)

We know that the tank will submerge a little further. This will increase the level of the water. Right?

by how much? Let us see

Let us assume mass of the container is m kg volume is V $m^3$

Volume submerged initially is $V_1{m}^3$

Then, $mg={\rho }_{\omega }{V}_{1}g\Rightarrow m={\rho }_{\omega }{V}_1$ - - - - - - (i)

After a volume of $V_2$ is added, let us assume, the volume of container now submerged is $V_3$

From Free body diagram,

$mg+{\rho }_{\omega }{V}_{2}g={\rho }_{\omega }{V}_{3}g$

$\Rightarrow m+{\rho }_{\omega }{V}_2={\rho }_{\omega }{V}_3$

$\Rightarrow {\rho }_{\omega }{V}_1+{\rho }_{\omega }{V}_2={\rho }_{\omega }{V}_3$ (from (i))

$\Rightarrow V_1+V_2=V_3$

Rise in volume of water = $V_3-V_1=V_2$

$\therefore$ The level of water will rise by $V_2{m}^3$

Now if the $V_2$ volume was taken from the tank itself, the rise will be zero.

$\therefore$The level will remain unchanged