Question

A body of mass 100 kg and density 500 \[kg/{{m}^{3}}\]floats in water. The additional mass should be added to the body so that the body will sink is going to be
A- 80kg
B- 100kg
C- 150kg
D- 200kg

Answer 1

Hint: When a body is placed in water it will float or sink is governed by the Archimedes principle. Also, there is another law called the law of floatation which determines how the body will float on water.

Complete step by step answer:
Archimedes principle states that the upward buoyant force that is exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaced.

The density of a body is given by, \[\rho =\dfrac{mass}{volume}\]
\[\rho =\dfrac{m}{v}\]------(1)
This shows that the density of a body can be increased by increasing the mass of the body. An object sinks in water if its density is greater than that of water. An object floats in water if its density is less than that of water.
Given mass=100 kg
Density of body=500 \[kg/{{m}^{3}}\]
The volume of the body using Eq (1) is given by, \[\dfrac{100}{500}=0.2\]\[{{m}^{3}}\]
Weight of water displaced= volume of body \[\times \]g\[\times \]density of water
=0.2\[\times \]1000\[\times \]g
=2000g Kg-wt
Mass of water displaced= 200kg
Therefore, the additional mass which can be added to the body, so that body can sink
=200−100=100kg

So, the correct answer is “Option B”.

Note:
In everyday language, weight and mass are interchangeably used widely. But in physics, they have distinct meanings. Mass is a constant quantity and has a constant value everywhere whereas weight is the gravitational force with which the body is attracted towards itself.