Question

A body having relative density $ 0.9 $ and volume $ 18cc $ has some iron pieces pierced into it. If it floats completely just completely immersed then the mass of the iron rod pieces present in it is
(A) $ 4g $
(B) $ 3.2g $
(C) $ 2.4g $
(D) $ 1.8g $

Answer 1

Hint: We are using the concept of buoyancy to solve this question. When an object is immersed in a fluid partly or wholly a force is exerted. So basically, when we try to immerse an object in water it an upward thrust is applied by the fluid on the object. This upward force which makes the object to float is called buoyant force.
Floating principle of any object can be described using Archimedes Principle which states that the upward buoyant force that is exerted on a body immersed in a fluid whether partially or fully submerged, is equal to the weight of the fluid that displaces and acts in the upward direction at the centre of the mass of displaced fluid.

Complete step by step solution:
Weight of water displaced equals weight of the body and weight of the iron pieces this is according to Archimedes principle.
 $ {\text{Weight of water displaced = Weight of body + Weight of iron}} $
 $ {\text{Relative density = }}\dfrac{{{\text{Density of object}}}}{{{\text{Density of water}}}} $
 $ \Rightarrow {\text{Mg = mg + }}{{\text{m}}_1}{\text{g}} $
Let m be the mass of iron.
 $ \Rightarrow {\text{V}} \times \rho \times g = {\text{mg + v}} \times \rho \times {\text{g}} $
 $ \Rightarrow 1 \times 18 = {\text{m + 0}}{\text{.9}} \times {\text{18}} $
 $ \Rightarrow {\text{m = 0}}{\text{.1}} \times {\text{18}} $
 $ \Rightarrow {\text{m = 1}}{\text{.8g}} $
Hence option D is the correct answer.

Additional Information:
The point where the force of buoyancy acts is called the centre of buoyancy. As we have discussed, upthrust is the upward force exerted on an object which is partially or fully immersed in a fluid.
If an object whose density is greater than that of the fluid in which it is submerged it tends to sink. If the object is less dense than the fluid then the upthrust can help to keep the object float.
If the relative density is greater than one then the object will sink in water and if the relative density is less than one then the object will sink.
The buoyant force depends on the volume of the body immersed and the density of the fluid.

Notes
Main applications of buoyancy are used in submarines. It sinks by letting water into its ballast tank so that weight can become equal to buoyant force.
Ship: It floats on the surface of sea when the volume of water displaced becomes equal to the weight of the ship. It is constructed in such a way that its density is less than that of the water.