Class 7 PHYSICAL QUANTITY & MEASUREMENT

1. Measurement of volume (3D concept)
2. Measurement of area (Estimate the area of irregular shape objects using graph paper)
3. Measurement of density of regular solid: Basic concepts, Formula,Simple Numericals
4. Calculation of speed: Basic oncept, Formula, Simple Numericals

1. WELCOME TO MY CLASS Mr. Souvik Chatterjee M.Sc (Physics)& B.Ed

2. PHYSICAL QUANTITY & MEASUREMENT Measurement of volume(3D Concept) Concept Of unit volume Measurement of area: Estimate the area of irregular shape objects using graph paper Measuirement of density of regular solids: Basic concepts, Formula, Simple Numericals (S.I unit not required Calculation of speed: Basic Concept, Formula, Simple Numericals (S.I unit not required)

3. KEY POINTS Measurement is a process of comparision of the given unknown quantity with a fixed known quantity of the second kind called unit Magnitude= Number of times the unit is contained in the quantity X Unit Length is the distance between two points. Its S.I unit is metre (m). It is measured with the help of a metre rule or measuring tape. Mass is the quantity of matter contained in the body. Its S.I unit is kilogram (kg). It is measured by a beam balance or an electronic balance. Time is the interval of occurrence of an event. Its S.I unit is second (s). It is measured with the help of a pendulum clock or a stop watch or stop-clock Temperature is a quantity which measures the hotness and coldness of a body. Its S.I unit is kelvin (K). It is measured using a thermometer .

4. MEASUREMENT OF VOLUME The space occupied by an object is called volume S.I unit of volume is cubic metre (m 3 ) Cubic metre is the volume of a cube with each side 1 meter long 1 m 3 = 1m X 1m X 1m Cubic centimetre is the volume of cube with each side 1 centimeter 1 cm 3 = 1 cm X 1 cm X 1 cm 1 m 3 = 1 m X 1 m X 1 m = 100 cm X 100 cm X 100 cm =1000000 cm 3 = 10 6 cm 3 The volume of a liquids is generally expressed in litre (L) 1 litre = 1000 cm 3 1 cm 3 = 1 mL

5. VESSELS FOR MEASURING THE VOLUME OF LIQUIDS Measuring Cylinder

6. Measuring Beaker

7. IMPORTANT FORMULA Volume of Cube=(One side) 3 Volume of Cuboid = Length X Breadth X Height Volume of a sphere =4/3 X ∏ X (radius) 3 Volume of a cylinder=∏ X (radius) 2 X Height Volume of a Cone = ∏/3 X (radius) 2 X Height Where ∏=3.141 or 22/7

8. NUMERICAL PROBLEM Problem-1 . A box of dimensions 1.5 cm X 2.0 cm X 90.0 cm. Find the volume of the box in ( i ) m 3 (ii) cm 3 ( i ) Volume= (1.5 X 2.0 X 90.0)= 270 cm 3 1 cm 3 = 1/1000000 m 3 (ii) 270 cm 3 = 270/1000000=0.00027 m 3

9. Problem-2 . A cylinder has length 80 cm and radius 2 m. Find vo lume in ( i ) m 3 (ii) cm 3 Ans . ( i ) length= 80 cm= 80/100= 0.8 m Volume= ∏ X 2 X 2 X 0.8 = 10.05 m 3 1 m 3 = 100000 cm 3 (ii)10.05 m 3 = 10.05 X 1000000 cm 3 = 10050000 cm 3

10. Problem 3 -A measuring cylinder contains water to a level 0f 20 mL. The water level rises to 50 mL. When a piece of copper is completely immersed in it. Find the volume of copper piece in ( i ) cm 3 (ii) m 3 Ans. ( i ) Volume= (50 − 20) mL = 30 mL = 30 cm 3 (ii) 30 cm 3 = 20/1000000 m 3 = 0.00003 m 3

11. HOME WORK 1. What is measurement? 2. What is unit? 3. How is the magnitude of a quantity expressed? 4. Define and state the unit of the following: (a)Length (b)Mass (c)Time (d)Temperature

12. 5. Define volume. State its S.I unit. 6. Define S.I unit of volume. 7. Define 1 cubic cm. Establish the relation between cubic meter and cubic centimeter. 8. State the unit by which volume of liquid is expressed? State its relation with cubic centimeter 9. State the instruments by which volume of liquid can be expressed. 10. State the formulas: (a) Volume of a cube (b) Volume of a cuboid (c) Volume of a sphere (d) Volume of a cylinder (e) Volume of a cone

13. MEASUREMENT OF AREA The surface occupied by an object is called its area. S.I unit of area is square metre (m 2 ) 1 m 2 is the area of a square of side 1m Bigger units of area are square decametre (or are) ,hectare and square kilometre . One are is the area of a square with each side measuring 10 m. 1 are = 100 m 2 One hectare is the area of a square with each side measuring 100 m. 1 hectare = 10000 m 2 = 100 are One kilometre square (km 2 ) is the area of a square of each side measuring 1 km. 1 km 2 = 1000000 m 2 To express area of small objects like pencil, rubber etc square metre is a big unit. The smaller units of area are square centimetre (cm 2 ) or square millimetre (mm 2 ). 1 cm 2 = 1/10000 m 2 1 mm 2 = 1/1000000 m 2

14. FORMULA Area of a sphere= (one side) 2 Area of a rectangle= Length X Breadth Area of a circle= ∏ X (radius) 2 Surface Area of a cylinder = 2∏ X (radius) X length Surface area of a sphere = 4∏ X (radius) 2

15. NUMERICAL PROBLEM Numerical-4 The diameter of a circular park is 140 cm. Find the surface area in ( i ) cm 2 (ii) m 2 Radius= 140/2= 70 cm ( i )Area= ∏ X (radius) 2 = (22/7 X 70X70)cm 2 =(22 X 10X70)=15400 cm 2 (ii)=15400/10000=1.54 m 2

16. Numerical-5 Find the area of a cylinder of radius 1m and length 210 cm. Find the area in ( i ) cm 2 (ii) m 2 Length= 210 cm= 2.1 m Area= ∏ X 1 X1 X 2.1= (22/7 X 2.1) =(22 X 0.3)=6.6 m 2 6.6 m 2 = 6.6 X10000 = 66000 cm 2

17. DENSITY Density of a substance is defined as the mass of a unit volume of that substance. S.I unit of density kilogram/metre 3 (kg/ m 3 ) C.G.S unit of density gram/centimetre 3 (g/cm 3 ) 1 g/cm 3 =1000 kg/ m 3 1 kg/m 3 = 1kg/ 1m 3 =1000g/(100) 3 cm 3 = 1g/1000 cm 3 = 1/1000 g/cm 3 1 g/cm 3 = 1000 kg/m 3 Density of copper is 8.9 g/cm 3 means ‘ The mass of of copper having volume 1cm 3 is 8.9 gram ’

18. NUMERICAL PROBLEM Numerical-6 Refer to the problem-3. If the mass the substance is 234 g. Find the density in ( i ) g cm -3 (ii) kg m -3 . Identify the substance. From the numerical- 3 volume = 30 ml= 30 cm 3 Density= 234/30= 7.8 g cm -3 = 7.8 X 1000 = 7800 kg m -3 The substance is iron

19. Numerical-7 The mass of a wooden block is 86 g. If the density of wood is 800 kg m -3 . Find the volume of block. Density = 800 kg m -3 = 800/1000 g cm -3 = 0.8 g cm -3 Volume = 86/0.8 = 107.5 cm 3

20. SPEED The distance travelled by the body in unit time is called speed of the body. S.I unit of speed is metre /second(m/s) Some times we measure speed in kilometre / hour(km/h) 1 m/s= 3.6 km/h or 5 m/s=18 km/h Speedometre of a vehicle such as scooter, car shows the speed of the the vehicle at that instant.

21. 1 km/h= 1 km/ 1 hour = 1000 m/3600 s = 1000/3600 X 1m/1s = 5/18 X 1m/s 18 km/h = 5 m/s Numerical-8 Convert the following speeds in m/s (a) 5 km/min (b) 54 km/h (a) 6 km/min = 6000 m/60 s = 6000/60 X 1m/1s= 100 X 1 m/s = 100 m/s (b) 54 km/h = 54 X 5/18 = 15 m/s

22. Numerical-9 A cyclist is moving with a speed of 30 km/h. How long will he take to travel a distance of 900 m? Distance = 900 m = 900/1000 = 0.9 km Time = distance/ speed = 0.9/30 = 0.03 h = 0.03 X 3600 s = 108 s.

23. HOME WORK Define area. State and define its S.I unit. Define: (a) one are (b) one hectare (c) one square kilometer. How is each of them related to S.I unit of area. State the formula: (a) Area of a square (b) Area of a rectangle (c) Area of a circle (d) Surface area of a cylinder (e) Surface area of a sphere.

24. Define density. State its S.I unit. State the use of barometer? Define speed. State its S.I unit. Establish the relation between meter per second and kilometer per hour.

25. NUMERICALS FROM CONCISE PHYSICS 1.The length, breadth and height of a water tank are 5m, 2.5m and 1.25m respectively. Calculate the capacity of the water tank in (a) cm 3 (b) litre (a) Capacity of the water tank= volume of the water tank = (5 X 2.5 X 1.25) = 15.625 m 3 (b) 1 m 3 = 1000 litre 15.625 m 3 = 15.625 X 1000 = 15625 litre

26. 2.A solid silver piece is immersed in water contained in a measuring cylinder. The level of water rises from 50 ml to 62 ml. Find the volume of silver piece. Ans. Volume of the silver piece = (62 − 50) [1 ml = 1 cm 3 ] = 12 ml = 12 cm 3 3.Find the volume of a liquid present in a dish of dimensions 10 cm X 10 cm X 5 cm. Ans. Volume of liquid = Volume of dish = (10 X 10 X 5) = 500 cm 3

27. 4.A rectangular field is of length 60 m and breadth 35 m. Find the area of the field. Ans. Area of the rectangle = (60 X 35) = 2100 m 2 6. A piece of brass of volume 30 cm 3 has a mass of 252 g. Find the density of brass in ( i ) g/cm 3 (ii) kg/m 3 Ans ( i ) Density = 252/30 = 8.4 g/cm 3 (ii) 8.4 X 1000 = 8400 kg/m 3

28. 7.The mass of an iron ball is 312g. The density of iron is 7.8 g/cm 3 . Find the volume of the ball. Ans. Volume of the ball = 312/7.8 = 40 cm 3 8. A cork has volume 25 cm 3 . The density of the cork 0.25 g/cm 3 . Find the mass of the cork. Ans. Mass of the cork = (25 X 0.25) = 6.25 g. 9. Mass of 5 litre of water is 5 kg. Find the density of in g/cm 3 . Volume = 5 L = 5000 ml = 5000 cm 3 [1 ml = 1 cm 3 ] Mass = 5 kg = 5000 g Density = 5000/5000 = 1 g/cm 3

29. 10. A cubical tank of side 1 m is filled with 800 kg of a liquid. Find: ( i ) The volume of the tank, (ii) the density of the liquid in kg/m 3 Ans.( i ) Volume= (1) 3 m 3 = 1 m 3 (ii)Density = 800/1 = 800 kg/m 3 11.A block of iron has dimensions 2m X 0.5m X 0.25m. The density of iron is 7.8 g/cm 3 . Find the mass of the block. Ans. Volume = (2 X 0.5 X 0.25) = 0.25 m 3 Density = 7.8 X 1000 = 7800 kg/m 3 Mass = 7800 X 0.25 = 1950 kg

30. 12.The mass of a lead piece is 115 g. When it is immersed into a measuring cylinder, the water level rises from 20 ml mark to 30 ml mark. Find: ( i ) The volume of the lead piece (ii) The density of the lead in kg/m 3 Ans. ( i ) Volume of the lead piece = (30 − 20) ml = 10 ml = 10 cm 3 (ii) Density = 115/10 = 11.5 g/cm 3 = (11.5 X 1000) = 11500 kg/m 3

31. 13. The density of copper is 8.9 g/cm 3 . What will be its density in kg/m 3 ? Ans.8.9 g/cm 3 = 8.9 X 1000 = 8900 kg/m 3 . 14. A car travels a distance of 15 km in 20 minutes. Find speed of the car in ( i ) km/h (ii) m/s. Ans.( i ) Time = 20 minutes = 20/60 = 1/3 hour Speed of car = 15/ (1/3) = 15 X 3= 45 km/h (ii) 45 km/h = 45 X (5/18) = 12.5 m/s

32. 15.How long a train will take to travel a distance of 200 km with a speed of 60 km/h? Ans. Time = 200/60 = 10/3 hour = (10/3 X 60) minute = 200 minutes = 3 h 20 mins 16. A boy travels with a speed of 10 m/s for 30 minute. How much distance does he travel? Ans. Time = 30 minute = (30 X 60) = 1800 s Distance = (10 X 1800) = 18000 m = 18 km.

33. 17.Express 36 km/h in m/s. Ans. 36 km/h = 36 X (5/18) m/s = 2 x 5 m/s = 10 m/s 18. Express 15 m/s in km/h. Ans. 15 m/s = 15 X (18/5) = 3 X 18 km/h = 54 km/h

34. IMPORTANT QUESTIONS How does density of water changes when (a)It is heated from 0 degree C to 4 degree C (b) It is heated from 4 degree C to 10 degree C Ans. ( i ) Increase Because of ANOMOLOUS Expansion Of WATER (ii) Decrease

35. A car travels with a speed 12 m/s, while a scooter travels with a speed 36 km/h, which of the two travels faster? Ans 36 km/h = (36 X 5/18) m/s = (2 X 5) m/s = 10 m/s Which is less than speed of car. So the car travels faster

36. THANK YOU