Question

A wooden block of mass 20 kg has density $800kg/m^3.$ What could be the maximum mass that can be placed on the wooden block so that the block floats just below the water surface?

• A.
  $30kg$
• B.
  $25kg$
• C.
  $5kg$
• D.
  $12kg$

Answer 1

The correct option is C

$5kg$
Mass of the wooden block, m = 20 kg

Let the maximum mass that can be placed on the block be x kg.
Total weight of the combination $=(20+x)g$

For the combination to float on water:

Upthrust exerted by water = weight of combination

$\Rightarrow m^{\prime }g=(20+x)g...\left(i\right)$
Here, m′ = mass of water displaced

$\Rightarrow {\rho }_w\times V\times g..\left(ii\right)$

Here, V = volume of the wooden block and ${\rho }_w$= density of water

$\Rightarrow V=\frac{\text{Mass of wooden block}}{\text{density of wooden block}}$
$\because \text{Density of the wooden block}=800kg/m^3$

Putting the value of V in equation (ii):
$20+x=1000\times \frac{20}{800}(\because {\rho }_w=1000kg/m^3)\Rightarrow 20+x=25\Rightarrow x=5kg$


Hence, the correct answer is option (c).