Unit-2. Properties of Matter. Solutions 2.1 Matter & Density page V 1 =4.3.6=72 cm 3. Volume of the removed triangular prism (V 2 )

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1 2.1 & Density page A solid object is given in the figure. Volume of the rectangular prism (V 1 ) V 1 =4.3.6=72 cm 3 Volume of the removed triangular prism (V 2 ) V 2 =((2.3)/2).6=18 cm 3 What is the volume of the solid object in cm 3? Volume of the solid(v) V=72-18=54 cm 3

2 2.1 & Density page The height of water column in a cylinder is 20 cm and the base radius of the cylinder is 2 cm. When a piece of stone is placed into the cylinder, the height of water column becomes 25 cm. (π=3) What is the volume of stone in dm 3? Volume of the cylindrical container (V) is equal to the volume of 12 semi spherical container or 6 spherical container. V=6.(4π.r 3 /3)=6.(4.3.r 3 /3)=24.r 3 V=π.r 2.h= =3000 cm 3 24.r 3 =3000 r 3 =125 then r=5 cm

3 2.1 & Density page A cylindrical container, whose radius and height are 10 cm, is going to be filled with water by using a semi sphere container. After filling and pouring the semi sphere 12 times, the cylindrical container becomes totally full. (π=3) What is the radius of the semi sphere? V one sugar cube =2.2.2=8 cm 3 (0,8 dm = 8 cm) V box =4.8.10=320 cm 3 number of sugar = 320 / 8 = 40

4 2.1 & Density page A football is made of plastic. The inner and outer radii of the sphere are 10 cm and 11 cm. (π=3) V inner =4π.r i3 /3= /3=4000 cm 3 V outer =4π.r o3 /3= /3=5324 cm 3 V plastic =V outer - V inner = What is the volume of the plastic that makes up the ball? V plastic =1324 cm 3

5 2.1 & Density page - 62 V one sugar cube =2.2.2=8 cm 3 5. How many sugar cubes, each is 2 cm along a side, can be placed in a rectangular prism whose dimensions are 4 cm, 0,8 dm and 10 cm? (0,8 dm = 8 cm) V box =4.8.10=320 cm 3 number of sugar = 320 / 8 = 40

6 2.1 & Density page A cylindrical container whose radius and height are 5 cm and 50 cm respectively is going to be filled with water by using a cubical cup, which is 5 cm along an edge. (π=3) How many cups of water are needed to fill the container completely? V cylincrical container =π.r 2.h= =3750 cm 3 V cylincrical container = =3750 cm 3 V cube =a 3 =5 3 =125 cm 3 number of cups = 3750 / 125 = 30

7 2.1 & Density page A cubic and a cylindrical containers are shown in the figure. The cubic container is completely filled with water. Then the water in the cube is poured into the cylinder. (π=3) Volume of cylindrical container is equal to the volume of the cube. V cylinder =V cube π.r 2.h=a 3 (22,5 mm =2,25 cm) ,25=a 3 27=a 3 then a=3 cm If the height of the water in the cylindrical container is 22,5 mm, what is the length of the cube along one side (a) in cm?

8 2.1 & Density page A dry sand sample has 30% air in it. Some amount of this dry sand is added into water. The water level rises from 70 ml to 105 ml. What is the volume of the dry sand sample in ml? V sand alone =105-70=35 ml 100 ml dry sand 70 ml sand V dry sand 35 ml sand V dry sand = (35.100)/(70)=50 ml

9 2.1 & Density page The equal-arm balances given in the figure are identical and they are in equilibrium as shown. The movement of rider between two successive divisions makes 1 g difference in mass. first balance; X=Y+(2.1) then X=Y+2 second balance; 2Y=X+(8.1) then 2Y=X+8 2Y=(Y+2)+8 What is the mass of object X in grams? Y=10 g then X= 12 g

10 2.1 & Density page The equal-arm balances given in the figures are identical and they are in equilibrium as shown. The movement of rider between two successive divisions makes 1 g difference in mass. 1st balance; X+Y=2Y+4 then X=Y+4 2nd balance; Z=X+Y+6 then Z=2Y+10 3rd balance; X+Z=2X+Y+R Z=X+Y+R 2Y+10=Y+4+Y+R R=4 th division Find the position of the rider for the third balance.

11 2.1 & Density page The-equal arm balance given in the figure is in equilibrium when three of the identical spheres are placed on the left pan; one of the identical spheres on the right pan and the rider is on the 4th division. Let s suppose that each division on the right arm refers to R grams. first case; 3X=X+4R then X=2R second case; 6X=2X+n.R (where n is the final position of the rider) If 6 of the identical spheres are placed on the left pan and 2 of them are placed on the right pan, what must the position of the rider be to adjust the balance again? 4.2R=n.R then 4X=n.R n=8 th division

12 2.1 & Density page The equal-arm balances are identical and in equilibrium as shown in figures. The sensitivity of the balances is 1 g/division. For Figure-1; X=2Y+2 then 2Y=X-2 For Figure-2; 2X=2Y+8 2X=X-2+8 X=6 g then Y=2 g X/Y = 6/2 = 3 What is the ratio of the mass of object X to the mass of object Y (m x /m y )?

13 2.1 & Density page The equal-arm balance is in equilibrium as shown in the figure. 12 g mass is removed from the right pan and the rider on the right arm is shifted to 8 th division. a) K=12+2.X K=8X 8X=12+2X X=2 g a) How many grams does the displacement of rider between two successive divisions refer to? b) K=8X K=2.8 K=16 g b) What is the mass of object K in grams?

14 2.1 & Density page The equal-arm balance shown in the figure is in equilibrium and the sensitivity of the balance is 0,1 g/division. The arms of the balance are divided into 10 equal divisions. Suppose that the position of the rider on the right arm is X. 14,3 = ,1.X 0,3 = 0,1.X X=3 rd division What is the position of the rider on the right arm?

15 2.1 & Density page The arms of a balance divided into 8 equally spaced divisions. The sensitivity of the balance is 800 mg and the balance is in equilibrium when the rider is set to 5 th division. 800 mg =0,8 g 6,7 = X + (5.0,8) 6,7 = X +4 X= 2,7 g What is the mass of object X in grams?

16 2.1 & Density page Equal-arm balances given in the figures are identical. The sensitivity of the balances is given as 1 g/division. For Figure-1; 16 = Y + (4.1) Y = 16-4 = 12 g What is the mass of object X in grams? For Figure-2; Y = X + (2.1) 12 = X +2 X = 10 g

17 2.1 & Density page A beaker is filled by water. The rate of flow of water from tap is constant. Plot the following graphs. 18. When a sample of liquid is heated in a closed container; (Suppose that no phase change and vaporization take place. Ignore the expansion of the container.) Fill in the blanks by using increases, decreases or remains the same. a) Mass of the liquid: remains the same b) Volume of the liquid: increases c) The distance between the liquid molecules: increases d) Number of liquid molecules in unit volume: decreases e) Density of the liquid: decreases

18 2.1 & Density page A sample of gas is trapped in a closed container. When the piston is pushed down slowly. a) Mass of the gas: remains the same Fill in the blanks by using increases, decreases or remains the same. a) Mass of the gas: b) Volume of the gas: decreases c) The distance between the gas molecules: b) Volume of the gas: decreases c) The distance between the gas molecules: d) Number of gas molecules in unit volume: increases d) Number of gas molecules in unit volume: e) Density of the gas: e) Density of the gas: increases

19 2.1 & Density page - 65 m container =440 g m container+water =480 g 20. The mass of an empty container is 440 g. When it is full of water, the total mass is 480 g. When it is full of a liquid, the total mass is 468 g. What is the density of the liquid? (Density of water is 1 g/cm 3.) m water = =40 g then V water =40 cm 3 V container =V water =40 cm 3 The liquid fills fully the same container. V liquid =40 cm 3 m container+liquid =468 g m liquid = =28 g then d liquid =(28 g).(40 cm 3 )=0,7 g/cm 3

20 2.1 & Density page - 66 m overflown liquid =30 g 21. A piece of stone of mass 180 g is immersed in a container that is full of a liquid of density 1,5 g/cm 3. The mass of the overflown liquid is 30 g. What is the density of the stone? V overflown liquid =(30 g)/(1,5 g/cm 3 )=20 cm 3 d object =(180 g)/(20 cm 3 ) d object =9 g/cm 3

21 2.1 & Density page When 120 g copper ball is immersed in a container that is full of water, 24 g water overflows from the container. a) What is the density of the copper ball? b) The density of the copper is 8 g/cm 3. What is the volume of the space in the copper ball? m overflown water =24 g then V overflown water =24 cm 3 d ball =(120 g)/(24 cm 3 ) d ball =5 g/cm 3 V metal =(120 g)/(8 g/cm 3 )=15 cm 3 then V space =24-15=9 cm 3

22 2.1 & Density page - 66 m liquid-x =(0,75 g/cm 3 ).(40 cm 3 )=30 g cm 3 of liquid X whose density is 0,75 g/cm 3 is mixed with 60 cm 3 of liquid Y of density 0,6 g/cm 3. What is the density of the mixture in terms of g/cm 3? m liquid-y =(0,6 g/cm 3 ).(60 cm 3 )=36 g d mixture =(30+36)/(40 +60) d mixture =66/100 d mixture =0,66 g/cm 3

23 2.1 & Density page The mass-volume graphs of liquids A and B are given. 40 cm 3 of liquid A and 60 g of liquid B are mixed. d A =(80 g)/(20 cm 3 )=4 g/cm 3 d B =(40 g)/(40 cm 3 )=1 g/cm 3 V A =40 cm 3 then m A =160 g m B =60 g then V B =60 cm 3 d mixture =( )/(40+60) d mixture =2,2 g/cm 3 What is the density of the mixture in g/cm 3?

24 2.1 & Density page - 66 For container-a; 25. The density of the liquid in container-a is 1,2 g/cm 3 and the container-b is empty. When the solid object X is dropped into the container-a, the mass of container-a increases by 270 g and the mass of container-b increases by 60 g. increases in mass = m X - m overflown liquid 270 = m X - 60 m X = 330 g For container-b; increases in mass = m overflown liquid 60 = m overflown liquid m overflown liquid = 60 g V overflown liquid = (60/1,2) = 50 cm 3 What is the density of solid object X in g/cm 3? V X = = 110 cm 3 d X = (330 g) / (110 cm 3 ) d X =3 g/cm 3