Question

A block of wood is floating on water with its dimensions \[50cm{\text{ }}x{\text{ }}50cm{\text{ }}x{\text{ }}50cm\] inside water. The buoyant force acting on the block is X N. Find X. Take \[g{\text{ }} = {\text{ }}9.8{\text{ }}Nk{g^{ - 1}}.\]
A. \[1225\]
B. \[0.1225\]
C. \[121.5\]
D. \[1221\]

Answer 1

Hint:
To find the value of X, i.e., the buoyant force acting on the block, we will find the value of weight of water displaced by the block, by using the statement of Archimedes’ principle. Hence, after putting the values in the formula, we will get our required answer.

Complete step by step solution:
We have been given that a block of wood is floating on water with its dimensions \[50cm{\text{ }}\times {\text{ }}50cm{\text{ }}\times {\text{ }}50cm\] inside water. It is given that the buoyant force acting on the block is \[X{\text{ }}N.\] We need to find the value of X.
So, the volume of water displaced \[ = \;50cm{\text{ }} \times {\text{ }}50cm{\text{ }} \times {\text{ }}50cm{\text{ }}\]
\[\begin{gathered}
   = {\text{ }}\frac{{50}}{{100}}{\text{m }} \times {\text{ }}\frac{{50}}{{100}}m{\text{ }} \times {\text{ }}\frac{{50}}{{100}}m\; \\
   = 50{\text{ }} \times {\text{ }}50{\text{ }} \times {\text{ }}50{\text{ }} \times {\text{ }}{10^{ - 6}}\;{m^3} = {\text{ }}0.125\;{m^3} \\
\end{gathered} \]

We know that the density of water, \[\left( \rho \right){\text{ }} = {\text{ }}1000\;kg\;{m^{ - 3}}\]

We also know that the weight \[ = {\text{ }}mg = volume \times density \times g...........(\because mass = volume \times density)\]

Now, on putting the value in the above formula, we get

Weight of water displaced \[ = \;0.125\; \times 1000{\text{ }} \times {\text{ }}9.8{\text{ }}\]
\[ = {\text{ }}1225\;N\]

Since, according to Archimedes principle, the buoyant force acting on an object is equal to the weight of the liquid displaced.

Therefore, the buoyant force acting on the block is \[1225{\text{ }}N.\]


Thus, the value of X is \[1225,\] i.e.,
option (A) \[1225{\text{ }}N \] is correct.

Note:
We know that when an object is immersed in a liquid it always experiences an upward force, known as Buoyant Force. In the solution, we have mentioned about Archimedes principle, let us understand about it in detail. So, it states that the upward buoyant force that is exerted on a body immersed in a fluid, whether the body is fully or partially submerged, is equal to the weight of the fluid that the body displaces.