Question

A boat floating in a tank is carrying a number of large wooden blocks. If the wooden blocks are unloaded into water, what will happen to the water level?

• A. It will increase
• B. It will decrease
• C. It will remain constant
• D. It will depend upon the nature of blocks

Answer 1

Answer: (C)

It will remain constant

Let $M_1$ be the mass of the boat and $M_2$ be mass of the wooden blocks.
When the blocks are lying in the boat. Let $\rho$ is the density of water, then volume of water displaced by the boat and blocks.
$V=\frac{(M_1+M_2)g}{g\rho }....\left(i\right)$
When the wooden blocks are unloaded into water, volume of water displaced by boat $V_1=\frac{M_{1}g}{\rho g}$ and volume of water displaced by the wooden blocks $V_2=\frac{M_{2}g}{\rho g}$
Therefore, the total volume of water displaced by the boat and block
$V^{\prime }=V_1+V_2=\frac{M_{1}g}{\rho g}+\frac{M_{2}g}{\rho g}....\left(ii\right)$
From (i) and (ii), we get
The volume of water displaced in the same. Hence the water level remain the same.