Question

A raft of wood (density $600\,kg{m^{ - 3}}$ ) of $120\,kg$ floats in water. How much weight can be put on the raft to make it “just sink”?
A. $40\,kg$
B. $80\,kg$
C. $120\,kg$
D. $200\,kg$

Answer 1

Hint:Here we have to use the concept of buoyancy. First we have to find the upthrust on the raft when it is just immersed. Also we can find the additional weight from the fact that the weight of the raft with additional weight is equal to upthrust while the raft neither sinks or floats.

Complete step by step answer:
The pressure exerted by the fluid in which an object is submerged causes the buoyancy force. As the friction of a fluid increases with depth, the buoyancy force often points upwards.

Buoyancy is directly proportional to the mass of the submerged fluid, or the buoyant force.
The theory of Archimedes states that a buoyant force equal in magnitude to the force of gravity on the displaced fluid is encountered by an object submerged in a fluid.

The theory of Archimedes is very useful for measuring an object's volume that does not have a normal form. It is possible to submerge the strangely shaped object, and the volume of the fluid displaced is equal to the object's volume. It may also be used in the measurement of an object's mass or specific gravity.

For e.g., the material should be weighted in air and then weighed when immersed in water for an object denser than water. When the object is submerged, it weighs less because of the buoyant force pushing upward. The object's specific gravity is then the object's weight in air divided by how much weight the object loses when placed in water.
Given,
Mass of raft $ = 120\,kg$, Density of wood $ = 600\,kg{m^{ - 3}}$
Volume of the raft $= \dfrac{{12}}{{600}} \\$
Volume of the raft $= \dfrac{1}{5}\,{m^3} \\ $
When the raft is just immersed in water its up thrust force is:
$
\dfrac{1}{5} \times 100 \\
\Rightarrow 200\,kgf \\
$
Let the additional weight be $S\,kgf$. The weight of the raft with additional weight is equal to upthrust while the raft neither sinks or floats.
$
120 + S = 200 \\
\Rightarrow S = 200 - 120 = 80\,kg $

Hence, option B is the answer.

Note: Here we have to see whether all the units match or not. If any unit is not in standard form we need to convert them. Also we have to add the additional weight to the given mass of the raft otherwise the answer would be wrong.