**Physical Quantities and Measurements**

**(Periwinkle Physics)**

I. Fill in the blanks using the given words.

[time, mass, distance, shape, closely packed, volume]

1. __Volume__ is the amount of space occupied by an object.

2. The molecules of a dense substance are __closely packed__.

3. Liquids have a definite volume but not definite __shape__.

4. The density of a substance is the ratio of its __mass__ to its __volume__.

5. Speed is the ratio of __distance__ to __time__.

II. Tick the correct statements and correctly rewrite the wrong ones.

1. Area is a fundamental quantity. [F]

= Area is a derived quantity.

2. Areas and volumes of all shapes can be calculated using a mathematical formula. [F]

= Areas and volumes of all shapes cannot be calculated using a mathematical formula.

3. The SI unit of density is kg/m³. [T]

4. One litre is equal to 1000 cm³. [T]

5. The SI unit of speed is km/h. [F]

= The SI unit of speed is m/s.

III. Match the columns.

=

Column A |
Column B |
---|---|

1. Density. |
(a) 10⁻³ litre. [3] |

2. Speed. |
(b) length x breadth. [4] |

3. 1 millilitre. |
(c) use graph paper. [5] |

4. Area of rectangle. |
(d) mass per unit volume. [1] |

5. Area of irregular shape. |
(e) distance per unit time. [2] |

IV. Select the correct options.

1. The space occupied by a 3D body is its

(a) mass. [ ]

(b) area. [ ]

(c) volume. [✓]

(d) length. [ ]

2. Which of the following relations is correct?

(a) Mass = volume x density. [✓]

(b) Volume = mass x density. [ ]

(c) Density = mass x volume. [ ]

(d) Density = volume/mass. [ ]

3. 1m³ is equal to

(a) 10² cm³. [ ]

(b) 10⁴ cm⁵. [ ]

(c) 10³ cm³. [ ]

(d) 10⁶ cm³. [✓]

4. 1 kg/m³ is equal to -

(a) 1000 g/cm³. [ ]

(b) 100 g/cm³. [ ]

(c) 1/100 g/cm³. [ ]

(d) 1/1000 g/cm³. [✓]

5. 1 km/h is equal to -

(a) 1000 m/s. [ ]

(b) 100 m/s. [ ]

(c) 5/18 m/s. [✓]

(d) 18/5 m/s. [ ]

V. Answer the following questions.

1. What is meant by the term area? Explain a method to find the area of an irregular shape.

= Area is the space occupied by a flat object.

The area of an object of irregular shape cannot be calculated using a mathematical formula. One way in which it can be done is by using a graph paper.

For example, we will estimate the area of a leaf using a graph paper. First we have to place the graph paper on a table and place the leaf on it. Then we have to draw the outline of the leaf using a pencil, and remove the leaf from the graph paper. Now we have to count the number of complete squares of 1 cm² size enclosed by the outline. Let this number be x.

Then we also have to count the numbers of squares which are half or more than half enclosed in the boundary.

Let this number be y. Ignore the squares which are less than half enclosed by the outline.

Now the approximate area of the leaf will then be (x + y) cm².

2. What is meant by the volume of an object? How would you determine the volume of a cuboid?

= Volume is the amount of space occupied by a three-dimensional object.

The volume of a cuboid can be determined by a mathematical formula i.e. (l x b x h). Here l is length, b is breadth and h means height of the cuboid respectively.

3. Describe a method to determine the volume of a solid of irregular shape.

= The volume of an irregular solid cannot be calculated by a mathematical formula. It is measured indirectly by immersing the solid in a liquid and measuring the volume of the liquid displaced by the solid.

This activity will make the idea clear -

We need a measuring cylinder, water, string and solid of an irregular shape (e.g. a stone)

First of all, we have the fill the half of the measuring cylinder with water. We have to note down the water level form the scale marked on the cylinder. This is the volume of the water. Let this volume be V₁ = 50 ml.

Now we have to tie the stone with the string and dip the stone into the cylinder holding the string till it completely immersed in water. We can now see that the water level in the cylinder rises.

Now we have the read the water level on the scale. Let it be V₂ = 75 ml.

Hence, the volume of the stone V = V₂ - V₁ = (75 ml - 50 ml) = 25 ml = 25 cm. (as 1 ml = 1 cm)

4. What is meant by the density of a substance? Write its SI unit.

= Density of a substance is defined as mass per unit volume.

The SI unit of density is kg/m³ or kg m⁻³.

5. How would you determine the density of : (a) a cuboid, (b) an irregular solid, and (c) a liquid?

= We can determine the density of the given things by the following way -

(a) a cuboid - We can measure the volume of the cuboid as (length x breadth x height); its mass can be determined using a beam balance or electronic balance. Then we have to divide its mass by its volume, we get its density.

(b) an irregular solid - We can measure the volume of the irregular solid by the help of the measuring cylinder. Its mass can be determined using a beam balance or electronic balance. Then we have to divide its mass by its mass by its volume, we get its density.

(c) a liquid - We can measure the volume of the liquid by the help of the measuring cylinder. Its mass can be determined using a beam balance or electronic balance. Then we have to divide its mass by its mass by its volume, we get its density.

6. Define speed. What is its SI unit?

= Speed is defined as the distance covered by an object per unit time.

SI unit of speed is m/s.

VI. Distinguish between the following.

1. Area and volume.

=

Area |
Volume |
---|---|

Area is the extent of a two-dimensional figure or
shape. |
Volume is the amount of space occupied by a three-dimensional
object. |

SI unit of area is m². |
SI unit of volume is m³. |

2. Volume and capacity.

=Volume is the amount of space occupied by a three-dimensional object.

On the other hand, capacity of a container is the maximum volume of liquid it can hold.

3. Speed and velocity.

= Speed is the ratio of the distance travelled to the time taken.

On the other hand, velocity is the ration of the displacement of the object from its starting position to the time taken.

VII. Solve the following numericals.

1. A cubical block of iron has each side of 10 cm. If the density of iron is 8 g/cm³, what is the mass of the block?

= Here, each side is 10 cm.

Then, the volume of the cubical block is (10 x 10 x 10) cm³ = 1000 cm³.

D = 8 g/cm³;

V = 1000 cm³;

Mass = Density x Volume = 8 g/cm³ x 1000 cm³;

= 8000 gm; = 8 Kg.

Therefore, the mass of the block = 8 kg.

2. The density of aluminium is 2.7 g/cm³. A piece of aluminium has a mass of 108 g. What is its volume?

= Here,

D = 2.7 g/cm³;

M = 108 g;

Volume = Mass ÷ Density; = 108 g ÷ 2.7 g/cm³;

= 1080 g ÷ 2.7 g/cm³;

= 40 cm³;

Therefore, the volume is 40 cm³;

3. What will be the mass of 1 litre of mercury if the density of mercury is 13.6 g/cm³.

= Here,

Volume = 1 litre = 1000 cm³;

Density = 13.6 g/cm³;

Mass = Density x Volume; = (13.6 g/cm³ x 1000 cm³);

= 13.6 gm.

Therefore, the mass of 1 litre of mercury is 13.6 gm.

4. 1 litre of turpentine oil has a mass of 800 g. What is its density in : (a) g/cm³ and (b) kg/m³?

= Here,

Volume = 1 litre = 1000 cm³; = 0.001 m³;

Mass = 800 g; = 0.8 kg;

(a) Density = Mass ÷ Volume = 800 g ÷ 1000 cm³;

= 0.8 g/cm³;

(b) Density = Mass ÷ Volume = 0.8 kg ÷ 0.001 m³;

= 800 kg/m³;

5. A train is running at a speed of 50 km/h. How much time will it take to cover a distance of 300 km?

= Here,

Speed = 50 km/h;

Distance = 300 km;

Time = Distance ÷ Speed = 300 km ÷ 50 km/h;

= 6 h.

Therefore, It will take 6 hours.

6. A car covers a distance of 100 km in 2.5 h. What is its speed?

= Here,

Distance = 100 km;

Time = 2.5 h;

Speed = Distance ÷ Time = 100 km ÷ 2.5 h;

= 40 km/h;

Therefore, Its speed is 40 km/h;

7. The speed of a car is 54 km/h. What is its speed in m/s?

= We know 1 km/h = 5/18 m/s;

so, 54 km/h = 54 x 5/18 m/s = 15 m/s;

Therefore, its speed in m/s is 15 m/s;

8. Calculate the area of the irregular shape shown in the figure. Assume each square has an area of 1 cm³.

= We should count all the complete, half and more than half squares enclosed in the boundary to get the area of the irregular shape.

Therefore, the area of the given shape is 28 cm³;