Question 1

Question 1Describe an experiment to determine the density of the material of a coin.

Accepted Answer

The density of the material of a coin is determined by the following experiment:We know density is mass per unit volume. So, first mass of the coin is measured by a common beam balance. Let it be M gram.Volume of the coin is measured by a measuring cylinder as shown in the figure given below.Take a measuring cylinder and fill it partly with water.Note the level of water. Let it be V1 mL.Tie the coin with a thread and gently lower the coin inside the measuring cylinder. Take care that no water splashes out.Note the level of water again. Let it be V2 mL.Find the volume of the coin (V) by subtracting V1 from V2.V = V2 - V1Density of coin is calculated by the formula: Density=MassVolume	ext{Density} = \dfrac{	ext{Mass}}{	ext{Volume}}Density=VolumeMass​D=MV g cm−3	ext{D} = \dfrac{	ext{M}}{	ext{V}}{	ext{ g cm}^{-3}}D=VM​ g cm−3

Question 2

Question 3What is a density bottle? How is it used to find the density of a liquid?

Accepted Answer

A density bottle is a specially designed bottle which is used to determine the density of a liquid. The figure of density bottle is shown below:Determination of Density of a Liquid using the Density BottleMeasure the mass of empty density bottle using a beam balance. Let it be M1 g.Remove the stopper of the bottle and fill it with water. Replace the stopper, wipe the outside of bottle dry and measure its mass again. Let it be M2 g.Empty the bottle and dry it. Fill it with the given liquid, replace the stopper and wipe the outside of bottle dry. Measure its mass. Let it be M3 g.Calculate the mass of water (M2 - M1) and the mass of liquid (M3 - M1).Since density of water is 1 g cm-3, mass of water contained in bottle is the volume of bottle. Thus,    Mass of liquid = M3 - M1    Volume of liquid = M2 - M1∴Density of liquid=Mass of liquidVolume of liquid=M3−M1M2−M1 g cm−3\therefore \text{Density of liquid} = \dfrac{\text{Mass of liquid}}{\text{Volume of liquid}} \[1em] = \dfrac{\text{M}_{3}-\text{M}_{1}}{\text{M}_{2}-\text{M}_{1}}{\text{ g cm}^{-3}}∴Density of liquid=Volume of liquidMass of liquid​=M2​−M1​M3​−M1​​ g cm−3

Question 3

Question 4The density of alcohol is 600 kg m-3. Express it in g cm-3.

Accepted Answer

Density of alcohol in g cm−3=Density of alcohol in kg m−31000=6001000=0.6 g cm−3\text{Density of alcohol in g cm}^{-3} = \dfrac{\text{Density of alcohol in kg m}^{-3}}{\text{1000}} \[1em] = \dfrac{600}{1000} = 0.6 \text{ g cm}^{-3}Density of alcohol in g cm−3=1000Density of alcohol in kg m−3​=1000600​=0.6 g cm−3Hence, Density of Alcohol in g cm-3 = 0.6 g cm-3.

Question 4

Question 5A piece of zinc of mass 438.6 g has a volume of 86 cm3. Calculate the density of zinc.

Accepted Answer

Mass of zinc = 438.6 gVolume of zinc = 86 cm3Density of zinc = ?Density of Zinc=Mass of ZincVolume of Zinc=438.686=5.1 g cm−3\text{Density of Zinc} = \dfrac{\text{Mass of Zinc}}{\text{Volume of Zinc}} \[1em] = \dfrac{\text{438.6}}{\text{86}} = 5.1 \text{ g cm}^{-3}Density of Zinc=Volume of ZincMass of Zinc​=86438.6​=5.1 g cm−3So, Density of Zinc = 5.1 g cm-3.

Question 5

Question 6A piece of wood of mass 150 g has a volume of 200 cm3. Find the density of wood in(a) C.G.S. unit(b) S.I. unit

Accepted Answer

Mass of wood = 150 gVolume of wood = 200 cm3Density of wood = ?(a) C.G.S. unit of density is g cm-3.Density of Wood=Mass of WoodVolume of Wood=150200=0.75 g cm−3\text{Density of Wood}= \dfrac{\text{Mass of Wood}}{\text{Volume of Wood}} \[1em] = \dfrac{\text{150}}{\text{200}} = 0.75 \text{ g cm}^{-3}Density of Wood=Volume of WoodMass of Wood​=200150​=0.75 g cm−3Density of wood = 0.75 g cm-3.(b) S.I. unit of density is kg m-3.Density of Wood in kg m-3 = Density of Wood in g cm-3 x 1000 = 0.75 x 1000 = 750 kg m-3So, Density of Wood = 750 kg m-3.

Question 6

Question 7Calculate the volume of wood of mass 6000 kg if the density of wood is 0.8 g cm-3.

Accepted Answer

Density of wood = 0.8 g cm-3 or 800 kg m-3Mass of wood = 6000 kgVolume of wood = ?Density of Wood=Mass of WoodVolume of WoodVolume of Wood=Mass of woodDensity of wood=6000800=7.5 m3\text{Density of Wood}= \dfrac{\text{Mass of Wood}}{\text{Volume of Wood}} \[1em] \text{Volume of Wood}= \dfrac{\text{Mass of wood}}{\text{Density of wood}} \[1em] = \dfrac{\text{6000}}{\text{800}} = 7.5 \text{ m}^3Density of Wood=Volume of WoodMass of Wood​Volume of Wood=Density of woodMass of wood​=8006000​=7.5 m3So, Volume of wood = 7.5 m3.

Question 7

Question 8Calculate the density of a solid from the following data:(a) Mass of solid = 72 g(b) Initial volume of water in measuring cylinder = 24 mL(c) Final volume of water when solid is completely immersed in water = 42 mL

Accepted Answer

Mass of solid = 72 gVolume of solid = Final volume of water - Initial volume of waterVolume of solid = 42 - 24 = 18 mLDensity of Solid=Mass of SolidVolume of Solid=7218=4\text{Density of Solid}= \dfrac{\text{Mass of Solid}}{\text{Volume of Solid}} \[1em] = \dfrac{\text{72}}{\text{18}} = 4Density of Solid=Volume of SolidMass of Solid​=1872​=4So, Density of solid = 4.0 g cm-3.

Question 8

Question 9The mass of an empty density bottle is 21.8 g, when filled completely with water it is 41.8 g and when filled completely with liquid it is 40.6 g. Find:(a) the volume of density bottle.(b) the relative density of liquid.

Accepted Answer

Mass of empty density bottle (M1) = 21.8 gMass of bottle with water (M2) = 41.8 gMass of bottle with liquid (M3)= 40.6 g(a) Mass of water in bottle = M2 - M1 = 41.8 - 21.8 = 20 gDensity of water is 1 g cm-3, so volume of density bottle = 20 mL(b) Mass of liquid in bottle = M3 - M1 = 40.6 - 21.8 = 18.8 gR.D. of liquid=Mass of LiquidMass of eq. vol. of water=18.820=0.94\text{R.D. of liquid}= \dfrac{\text{Mass of Liquid}}{\text{Mass of eq. vol. of water}} \[1em] = \dfrac{\text{18.8}}{\text{20}} = 0.94R.D. of liquid=Mass of eq. vol. of waterMass of Liquid​=2018.8​=0.94Relative density of liquid = 0.94.

Question 9

Question 10From the following observations, calculate the density and relative density of a brine solution.Mass of empty density bottle = 22 gMass of bottle + water = 50 gMass of bottle + brine solution = 54 g

Accepted Answer

Mass of empty density bottle (M1) = 22 gMass of bottle + water (M2) = 50 gMass of bottle + brine solution (M3) = 54 gMass of water in bottle = M2 - M1 = 50 - 22 = 28 gDensity of water is 1 g cm-3, so volume of density bottle = 28 cm3.Mass of brine solution in bottle = M3 - M1 = 54 - 22 = 32 gDensity of brine soln.=Mass of brine soln. Vol. of brine soln.=3228=1.14 g cm−3\text{Density of brine soln.}= \dfrac{\text{Mass of brine soln.}}{\text{ Vol. of brine soln.}} \[1em] = \dfrac{\text{32}}{\text{28}} = 1.14 \text{ g cm}^{-3}Density of brine soln.= Vol. of brine soln.Mass of brine soln.​=2832​=1.14 g cm−3So, density of brine solution = 1.14 g cm-3.R.D. of brine soln.=Mass of brine soln.Mass of eq. vol. of water=3228=1.14\text{R.D. of brine soln.}= \dfrac{\text{Mass of brine soln.}}{\text{Mass of eq. vol. of water}} \[1em] = \dfrac{\text{32}}{\text{28}} = 1.14R.D. of brine soln.=Mass of eq. vol. of waterMass of brine soln.​=2832​=1.14So, Relative density of brine solution is 1.14.

Question 10

Question 11The mass of an empty density bottle is 30 g, it is 75 g when filled completely with water and 65 g when filled completely with a liquid. Find:(a) Volume of density bottle,(b) Density of liquid and(c) Relative density of liquid.

Accepted Answer

Mass of empty density bottle (M1) = 30 gMass of bottle with water (M2) = 75 gMass of bottle with liquid (M3)= 65 g(a) Mass of water in bottle = M2 - M1 = 75 - 30 = 45 gDensity of water is 1 g cm-3, so volume of density bottle = 45 mL.(b) Mass of liquid in bottle = M3 - M1 = 65 - 30 = 35 gDensity of liquid=Mass of liquid Vol. of liquid=3545=0.77 g cm−3\text{Density of liquid}= \dfrac{\text{Mass of liquid}}{\text{ Vol. of liquid}} \[1em] = \dfrac{\text{35}}{\text{45}} = 0.77 \text{ g cm}^{-3}Density of liquid= Vol. of liquidMass of liquid​=4535​=0.77 g cm−3So, density of liquid = 0.77 g cm-3.(c) R.D. of liquid=Mass of liquidMass of eq. vol. of water=3545=0.77\text{R.D. of liquid}= \dfrac{\text{Mass of liquid}}{\text{Mass of eq. vol. of water}} \[1em] = \dfrac{\text{35}}{\text{45}} = 0.77R.D. of liquid=Mass of eq. vol. of waterMass of liquid​=4535​=0.77So, Relative density of liquid is 0.77.

Question 11

Question 1(b)The relative density of alcohol is 0.8. Its density is:0.8800 kg m-3800 g cm-30.8 kg m-3

Accepted Answer

800 kg m-3Reason —Relative density of alcohol=Density of alcoholDensity of water0.8=Density of alcohol1000 kg m−3Density of alcohol=0.8×1000=800 kg m−3\text{Relative density of alcohol} = \dfrac{\text{Density of alcohol}}{\text{Density of water}} \[1em] \text{0.8} = \dfrac{\text{Density of alcohol}}{\text{1000 kg m}^{-3}} \[1em] \text{Density of alcohol} = 0.8 \times 1000 = {\text{800 kg m}^{-3}}Relative density of alcohol=Density of waterDensity of alcohol​0.8=1000 kg m−3Density of alcohol​Density of alcohol=0.8×1000=800 kg m−3

Physical Quantities and Measurement

Exercise 2 Long Answer Type Questions

Exercise 2 Numericals

Exercise 2 Objective Type Questions