**Why Bodies Float? – Maharashtra Board Class 9 Solutions for Science and Technology (English Medium)**

**Solution 1:**

- A solid is completely immersed in a liquid. The force exerted by the liquid on the solid will be in vertically
direction.__upward__ - When an object sinks into the liquid, the density of object is
than density of the liquid.__greater__ - The
on unit surface area is called pressure.__thrust__ - The buoyant force is greater if density is
.__greater__ - The SI unit of pressure is
.__N/m__^{2}

**Solution 2:**

Column I |
Column II |
Column III |

1) Pressure | a) Thrust/ area |
i) Decreases with increase in area |

2) Density | b) Mass/ volume |
ii) Useful to determine purity of substance |

3) Atmospheric pressure | c) pascal | iii) Decreases with increase in height above sea level |

4) Relative density | d) No unit | iv) Specific gravity |

**Solution 3.1:**

No. The water will not overflow when the ice melts. Ice floats because it is less dense than liquid water. The volume of the water which the ice cube displaces is the same as the mass of water in the ice cube. As ice melts, the space occupied by the same amount of mass is less due to which the water level goes down.

**Solution 3.2:**

A block of plastic released under water will come up to the surface of water. When a block of plastic is under water, the magnitude of the buoyant force exerted by water on the block is greater than the magnitude of the weight of the block. So, the block will start moving upward. When it comes up partly above the water surface, the volume of the water displaced by the block becomes less, and at a certain stage, the buoyant force and weight balance each other. Then, the block continues to remain in that state, and the net force on the block becomes zero.

**Solution 4.1:**

- The buoyant force due to a liquid is proportional to the density of the liquid. When a body floats, the magnitude of the buoyant force acting on the body is equal to that of the weight of the body. Hence, the volume of the liquid displaced by a floating body is inversely proportional to the density of the liquid.
- The density of freshwater is less than that of seawater. Hence, a ship displaces a greater volume of freshwater relative to that of seawater. Therefore, ships entering freshwater from seawater sink to a greater extent.

**Solution 4.2:**

- The pressure due to a force is inversely proportional to the area on which it acts.
- The cutting edges of tools such as knives and blades are provided with sharp edges so that a large pressure can be produced and the object can be cut with ease and less force.

**Solution 5.1:**

- The lactometer and hydrometer are devices based on the Archimedes’ principle.
- The lactometer is a device used to determine the purity of a sample of milk. The extent to which a lactometer floats or sinks depends on the density of the milk, i.e. purity.
- The same thing is true for a hydrometer. The greater the density of a liquid, the less is the extent to which the body sinks in it.
- Archimedes’ principle is used in designing of ships and submarines. Submarine is a ship which can sink in the sea when necessary and reappear again on the surface of the sea. It is provided with a large tank both at the front and at the back. These tanks can be filled with seawater or air from compressed air reservoirs.
- The density of a body that floats or sinks in water or kerosene can be determined by Archimedes’ principle. The density of kerosene can be determined by Archimedes’ principle using the body of such a material which is not affected by water and kerosene.

**Solution 5.2:**

- When a body is immersed partially or completely in a liquid, the liquid exerts forces on all sides of the body. This force is perpendicular to the surface of the body and equal to the product of pressure and area at that point.
- The resultant of all these forces acts in the upward direction which is known as the upthrust or buoyant force.
- The buoyant force is proportional to 1) the volume of the liquid displaced by a body 2) the density of the liquid 3) the acceleration due to gravity
- The magnitude of the buoyant force is equal to the magnitude of the weight of the liquid displaced by the body.

**Solution 6.A:**

Mass (kg) |
Volume (m^{3}) |
Density (kg/m^{3}) |

350 | 175 | 2 |

760 |
190 | 4 |

Solution 6.B:

(kg/m^{3}) |
Density of water (kg/m^{3}) |
Relative density |

5 × 10^{3} |
10^{3} |
5 |

8.5 × 10^{3} |
10^{3} |
8.5 |

**Solution 6.C:**

Thrust (N) |
Area (m^{2}) |
Pressure (N/m^{2}) |

800 |
0.04 |
20000 |

1500 |
500 |
3 |

**Solution 7.1:**

Data: Density of the metal = 10.8 × 10^{3} kg/m^{3},

density of water = 10^{3} kg/m^{3}, relative density of a metal = ?

**Solution 7.2:**

Data: F = 50 cm × 20 cm = 0.5 m × 0.2 m = 0.1 m^{2}, pressure = ?

The pressure acting at the bottom is 10^{4} N/m^{2}.