CBSE Class 9 Science Practical Skills – Density of Solid

CBSE Class 9 Science Practical Skills – Density of Solid

Basic Building Concepts
Density
It is the physical property of a matter that describes how the individual particles of the substance are closely packed together. In other words, it describes the degree of compactness of a substance.
In qualitative manner, the density of a substance is defined as its mass per unit volume, i.e.,
Density(ρ) = \(\frac { Mass(M) }{ Volume(V) }\)
The amount of matter contained in the body is called mass. The mass is measured commonly in grams (g) and its SI unit is kilogram (kg).
The space occupied by the quantity of matter is called volume of the object. It is measured in cubic centimetres (cm³) and its SI unit is m³.
Therefore, unit of density is g/cm³ or kg/m³
1 kg m^-3 = 10^-3 gcm^-3

You can also Download Class 9 Science Notes PDF to help you to revise complete Syllabus and score more marks in your examinations.

Density of Some Common Substances
The density of a given substance, under specified condition, is always the same. Therefore, it is a characteristic property. It is different for different substances as shown in the following table:

Substances	Densities
	g cm-3	kg m-3
Air	0.0013	1.30
Ice	0.92	920
Water	1.00	1000
Common Salt (NaCl)	2.16	2160
Aluminium	2.70	2700
Iron	7.80	7800
Silver	10.50	10500
Gold	19.30	19300

From the table, it is clear that the different substances have different densities. Thus density measurements provide a useful tool for identifying substances either molecules of a compound or atoms of an element.
The factor that can affect the density of a material is temperature. When the temperature of a substance increases, its density decreases.
Applications

• Categorise the substance.
• Identify the different materials.
• For building ships and making hot air balloons.
• Determine the purity of a substance.

Examples

• Ice floats on water.
• Oil floats on the surface of water.
• Stone sinks in liquid (water).

Relative Density
When density of a substance is compared with the density of water, then it is called relative density. Thus relative density of a substance is the ratio of its density to that of water at 4°C having the same volume as that of the substance.
Relative Density(R.D.) = \(\frac { Density\quad of\quad Substance({ \rho  }_{ s }) }{ Density\quad of\quad Water({ \rho  }_{ w })\quad at\quad { 4 }^{ 0 }C }\)
or
R.D. = \(\frac { { \rho  }_{ s } }{ { \rho  }_{ w } }\)
Since the relative density is expressed in terms of ratio, it has no unit.
If the relative density of a substance is more than 1, the substance would sink in water. For example, relative density of iron is 2.70, so it sinks in water.
If R.D. < 1, the substance or object floats on the surface of water. For example, ice block.

Spring Balance
It is simply a spring whose one end is attached to a rigid support and other free end with a hook attached to another object.
Working Principle of Spring Balance
It works on the principle of elasticity. Applied force to stretch a spring is directly proportional to the change in length from its mean position. Therefore, the scale marking on the spring scale are equally spaced. Mathematically,
F ∝ x
or F = -kx
where F is the force exerted by a spring, and x is the displacement of the end of a spring from its equilibrium position. The proportionality constant ‘k’ is called ‘spring constant’. More the spring constant, harder the spring to stretch out.
Negative sign indicates that applied force and spring stretched distance both are in opposite directions as shown below.

On hanging the object from the hook, spring will stretch. Let the change in length of spring be x. The mass of the object is pulled down by force of gravity (mg) and pulled up by the spring force (F). These forces balance each other, i.e., F = mg. Thus with the help of a spring, we can measure the weight of the body not the mass of the body. If the scale of spring balance is calibrated in gram, then the weight of solid is measured in gram-weight. Weight of the body in gram-weight is numerically equal to the mass of the solid.

Uses

• Spring balance or spring scale is used in physics as a basic accelerometer.
• For weighing heavy loads in industry.
• To measure the weight of materials carried on a conveyor belt.

Aim
To determine the density of a solid (denser than water) by using a spring balance and a measuring cylinder.

Apparatus Required
A metallic object (any shape), iron stand, a spring balance, a measuring cylinder (preferably 0-250mL)

Theory
Mass per unit volume of a substance is called the density of a given substance.
Let M be the mass of a given substance/object and V be its volume. Its density ρ is given by
ρ = \(\frac { M }{ V } =\frac { Mass\quad of\quad Object }{ Volume\quad of\quad Object }\)
Its S.I. unit is kg m^-3.
Let the weight of object measured by the spring balance in air = W g-wt.
Initial volume of water in measuring cylinder = V₁ mL.
Final volume of water in measuring cylinder when object is fully immersed in water = V₂ mL.
Volume of object = Volume of displaced water = (V₂ – V₁) mL
Therefore, density of object (ρ) = \(\frac { W }{ { V }_{ 2 }-{ V }_{ 1 } }\) g cm^-3

Procedure

1. Hang the spring balance vertically with the help of iron stand as shown in Fig. 2.2.
2. Find its least count by using the given formula:
   Least Count = \(\frac { Rangeofgiven\quad spring\quad balance }{ Total\quad number\quad ofdivisions }\)
3. Check the zero error (if any) and record it with proper sign.
   This is the reading of spring balance when no weight is suspended from its lower hook.
   
   Measurement of weight of a given metallic object:
4. Hang the metallic object with the lower hook of the spring balance as shown in Fig. 2.3.
5. Take the reading of spring balance when the metallic object becomes static.
6. Obtain the true weight of the given metallic object by subtracting the zero error (if any) from the observe weight.
7. Repeat the experiment thrice and find its mean weight.
   Measurement of the volume of a given metallic object:
8. Pour some water into the measuring cylinder and record the initial level of water (lower position of meniscus) as shown in Fig. 2.4. Let the initial volume be V₁ (mL).
9. Remove the metallic object from the spring balance and tie it by a thin strong thread and immerse it fully in the water in measuring cylinder.
10. Note down the new position of meniscus V₂ (mL) in the measuring cylinder as shown in Fig. 2.5. The level of water rises up because the immersed object displaces water from its initial level.
11. Obtain the volume of the immersed metallic object by subtracting the two position of meniscus (water level) i.e. V₂ – V₁
12. Repeat the experiment thrice and find its mean volume.
    

Observations
Least count of spring balance: ………… g wt.
Zero error of the spring balance: …………. g wt.
Least count of measuring cylinder: ……….mL
Table: Measurement of weight of a given metallic object.

S.No.	Reading of spring balance		Weight of metallic object
	(without object) W1 (g wt.)	(with object) W2 (g wt.)	Weight of object observed W2 – W1 (g wt.)	True weight of object W = (W2 – W1) – (Zero error) (g wt.)
1.				W’1 =
2.				W’2 =
3.				W’3 =

Mean weight of given metallic object = \(\frac { { W }_{ 1 }^{ ‘ }+{ W }_{ 2 }^{ ‘ }+{ W }_{ 3 }^{ ‘ } }{ 3 }\) = ………..g wt.
Mass of the given metallic object by spring balance, (M) = ………….. g.
Table: Measurement of volume of a given metallic object

S.No.	Initial position of meniscus (Without metallic object) V1 (mL)	Final position of meniscus (Metallic object immersed) V2 (mL)	Volume of object V = V2 – V1 (mL)
1.			V’1 =
2.			V’2 =
3.			V’3 =

 Mean volume V = \(\frac { { V }_{ 1 }^{ ‘ }+{ V }_{ 2 }^{ ‘ }+{ V }_{ 3 }^{ ‘ } }{ 3 }\) = ………….mL

Calculations
True mass of given object = ………… g
Volume of given object = …………..mL
Density of a given metallic object = \(\frac { Mass\quad of\quad Object }{ Volume\quad of\quad Object } =\frac { M }{ V }\) g/mL = ……….g/mL = ………… kg m^-3 ( 1000 kg m^-3 = 1 gmL^-1)

Result
The density of the given solid (heavier than water) = ……… kg m^-3.

Precautions

1. Spring balance should be sensitive, stable and error free.
2. The horizontal pointer should move freely along the scale of spring balance.
3. Spring balance must be suspended vertically from fixed support of iron stand.
4. Reading should be taken only when oscillation of hanging object dies completely.
5. Eye should be kept in line (exactly horizontal) while taking the reading of spring balance as well as measuring cylinder as shown in figs. 2.6 and 2.7.
6. Solid object should be dried completely before measuring mass in air and when allowed to immersed in water.
7. While measuring the volume of object, the object should not touch sides and bottom of a measuring cylinder.
8. The water of the measuring cylinder should not fall out during immersing of solid object.
   

Source of Error

1. Least count of spring balance may be higher.
2. Spring of spring balance may be permanently stretched.
3. Solid object may not be completely dried.
4. The eye may not be in the proper level of meniscus while measuring the volume of solid object.

Interactive Session

Question 1.
What is the aim of your object?
Answer:
To determine the density of a given solid (denser than water) by using spring balance and measuring cylinder.

Question 2.
What is the unit of density?
Answer:
g cm^-3 or kg m^-3.

Question 3.
What is the relation between mL and cm³?
Answer:
1 mL = 1 cm³.

Question 4.
Is there any effect of temperature on the density?
Answer:
Yes, density of a substance decreases with the rise in temperature.

Question 5.
Why?
Answer:
Due to rise in temperature, volume of the body increases and hence density decreases.

Question 6.
What is the density of water at 4°C?
Answer:
It is 10³ kg/m³ or 1 gm/cm³.

Question 7.
What is the difference between mass and weight?
Answer:
Mass is a measure of the quantity of matter, which is constant all over the universe. Weight is proportional to the mass but depends on the gravity of the planet.

Question 8.
What is weight?
Answer:
Weight is the force exerted on a body by gravitational attraction of the planet (earth).

Question 9.
Convert 500 g mass into unit of force.
Answer:
Unit of force is newton (N)
F = mg = \(\frac { 500\quad kg }{ 1000 } \times 9.8\) m/s² = 4.9 kg ms^-2 = 4.9 N

Question 10.
Name the device which measures the mass and weight.
Answer:
Mass is measured by physical balance. Weight is measured by spring balance.

Question 11.
What is the working principle of spring balance?
Answer:
The extension in the length of spring when the body is suspended from its free end, is directly proportional to the weight of the body.

Question 12.
You stated that weight was measured by spring balance, then how can you deduce mass from weight?
Answer:
The weight of the body in gram-weight is numerically equal to the mass of solid,
i. e., 100 gwt. = 100 gf = 100 g. or 100 kgwt. = 100 kg f = 100 kg.

Question 13.
How can we minimise the error in the measurement of volume of water in the measuring cylinder?
Answer:
We can use the measuring cylinder having a scale of less least count.

Question 14.
What change in volume of water observe when water is heated uniformly from 0°C to 100°C?
Answer:
The volume of water decreases upto 4°C and then further increases.

Question 15.
Which water has the lesser density River water or Sea water?
Answer:
River water.

NCERT Lab Manual Questions

Question 1.
Can you determine the density of a porous solid by using a spring balance and a measuring cylinder? Give reasons in support of your answer.
Answer:
No, we cannot determine the density of a porous solid by using a spring balance and a measuring cylinder because

1. the porous solid have a void space in the form of pores in it.
2. It will absorb some water.
3. absorption of water by the porous solid may affect the
   • change in its weight and
   • volume of water displaced by it.

Question 2.
How does the presence of an air bubble in the liquid taken in the measuring cylinder affect the volume of the solid?
Answer:
The presence of air bubble inside the water taken in the measuring cylinder increases the volume of water in the cylinder. This may affect the apparent change in volume of the solid.

Question 3.
Density of a sealing wax is 1.8 g/cm³, express it in kg/m³.
Answer:
Density of a sealing wax is 1.8 g/cm³
1.8 g/cm³ = \(\frac { { 1.8 }\times { 10 }^{ -3 } }{ ({ 10 }^{ -2 })^{ 3 } }\) kg/m3 = 1.8 x 10³ kg/m³

Question 4.
A metal cylinder is melted and the whole mass is cast in the shape of a cube. What happens to its density? Give reasons.
Answer:
In both the cases, (i) mass and (ii) volume of water displaced by the metallic cylinder and cube remain same. So mass per unit volume does not change. Hence the density of a cube will be equal to the density of the cylinder.

Question 5.
At which temperature is the density of water maximum?
Answer:
Density of water is maximum at 4°C because water when cooled contracts upto 4°C and it expands when cooled further below 4°C. (The density of water at 4°C = 1000 kg/m³)

Practical Based Questions

Multiple Choice Questions/VSA (1 Mark)

Question 1.
The density of which of the following cannot be measured accurately using a spring balance and a measuring cylinder? [CBSE 2010]
(a) A ball filled with a liquid having a leakage
(b) A block of ice at 0 °C
(c) A small porous solid
(d) All of these

Question 2.
You are given a sphere of radius 2 cm. If you are asked to select a best suited spring balance to determine its weight, then out of the following which one would you prefer? The sphere is made of an alloy of density 7 x 10³ kg m^-3. [CBSE 2011, 2010, NCT 2007]
(а) Range 0 – 1000 gwt, Least count 5 g wt
(b) Range 0 – 500 gwt, Least count 2.5 gwt
(c) Range 0 – 250 gwt, Least count 2.5 gwt
(d) Range 0 – 100 gwt, Least count 1 gwt

Question 3.
The water level in a measuring cylinder, before and after immersing a metal cube in it, is shown in the figure. The volume of the metal cube is: [CBSE 2010]

(a) 24 cm³
(b) 22 cm³
(c) 20 cm³
(d) 18 cm³

Question 4.
Four measuring cylinders with least count 2.5 ml, 1.0 ml and 0.5 ml and 0.2 ml are available. Which one should be preferred for finding the density of a solid accurately? The one having least count:
[CBSE 2011, 10]
(a) 2.5 ml
(b) 1.0 ml
(c) 0.5 ml
(d) 0.2 ml

Question 5.
Three students A, B and C noted the water level reading in the measuring cylinder, as shown in figure. The correct way of taking reading is of: [CBSE 2010]

(a) A and C
(b) Only B
(c) Only C
(d) A and B

Question 6.
In a spring balance the space between 0 and 25 g marks is divided into 10 equal parts. The least count of spring balance is: [CBSE 2010]
(a) 2.5 g wt
(b) 25 g wt
(c) 0.25 g wt
(d) 15 g wt

Question 7.
The least count of the spring balance shown in the diagram is: [CBSE 2010]

(a) 5 g
(b) 2 g
(c) 1 g
(d) 0.5 g

Question 8.
In the following figure the zero error is: [CBSE 2010]

(a) 2 g wt
(b) -2 g wt
(c) 5 g wt
(d) -5 g wt

Question 9.
If we want to determine the volume of a solid by immersing it in water, the solid should be
[CBSE 2010]
(a) lighter than water.
(b) heavier than water.
(c) insoluble in water.
(d) heavier than water and insoluble

Question 10.
The correct way of reading the liquid level is shown in [CBSE 2012, 2011]

(a) Figure A
(b) Figure B
(c) Figure C
(d) Figure D

Question 11.
A given solid is weighed in air using a spring balance. It is then weighed by immersing it fully, in each of the three different vessels A, B and C as shown. The weight of solid would be [CBSE 2012]

(a) more in vessel C
(b) more in vessel B
(c) more in vessel A
(d) equal in all the three vessels.

Question 12.
The level of water in a measuring cylinder before and after a solid of 8 g mass is fully immersed into it as shown.

The density of the given solid is: [CBSE 2012]
(a) 4 g/cm³
(b) 2 g/cm³
(c) 3 g/cm³
(d) None of these

Question 13.
The least count of the spring balance and the measuring cylinder respectively are: [NCT 2007]

(a) 1 g wt; 1 ml
(b) 1 g wt; 2 ml
(c) 2 g wt; 1 ml
(d) 2 g wt; 2 ml

Question 14.
A student performing the experiment ‘To determine the density of solid (denser than water), by using spring balance and measuring cylinder’. During the experiment, he observed that a few air bubbles are sticking to the solid when immersed in water. The presence of air bubbles will lead to
(a) no change in density
(b) increase in density
(c) decrease in density
(d) none of the above

Question 15.
A spring balance reads 10 kg when a bucket of water is suspended from it. An iron piece having some mass is suspended by another string and immersed in the bucket with half of its volume. The reading of balance will
(a) decrease
(b) increase
(c) remain the same
(d) another spring balance needed

Question 16.
While determining the density of a copper piece using a spring balance and a measuring cylinder, seema carried out the following procedure:
(i) Noted the water level in the measuring cylinder without the copper piece.
(ii) Immersed copper piece in water.
(iii) Noted the water level after immersing copper in the measuring cylinder.
(iv) Removed the copper piece from the water and immediately weighted it using a spring balance.
The wrong step in the procedure is:
(a) (i)
(b) (ii)
(c) (iii)
(d) (iv)

Question 17.

Four measuring cylinders with different least counts are shown in figures A, B, C and D respectively. The most suitable cylinder for determining the volume of a cube of side 1 cm is
(a) A
(b) B
(c) C
(d) D

Question 18.
While determining the density of a solid, a student is provided with four different combinations.
Measuring cylinder

S. No.	Range	Least count
1.	0 – 100 ml	1 ml
2.	0 – 200 ml	5 ml
3.	0 – 100 ml	2 ml
4.	0 – 200 ml	2 ml

 Spring balance

S. No.	Range	Least count
1.	0 – 100 g wt	1 g wt
2.	0 – 200 g wt	5 g wt
3.	0 – 100 g wt	2 g wt
4.	0 – 200 g wt	2 g wt

The student should prefer to choose combination
(a) 1-1
(b) 2-2
(c) 3-3
(d) 4-4

Question 19.
A student notes down the observations in two spring balances and the measuring cylinder shown in the figure. From the given observations, the volume of the solid is

(a) 64 cc
(b) 36 cc
(c) 28 cc
(d) 100 cc

Answers

1. (d)
2. (c)
3. (c)
4. (d)
5. (b)
6. (a)
7. (b)
8. (b)
9. (d)
10. (a)
11. (d)
12. (a)
13. (d)
14. (c)
15. (b)
16. (d)
17. (a)
18. (a)
19. (c)

Short Answer Questions (2 Marks)

Question 1.
Define relative density of a substance. Relative density of silver is 10.8. The density of water is 1000 kgm^-3. What is the density of silver in SI units?
Answer:
Relative density is defined as the ratio of density of a substance to the density of water. Therefore,
Relative density = \(\frac { Density\quad ofa\quad substance }{ Density\quad of\quad water }\)
Density of silver = Relative density of silver x Density of water
= 10.8 x 1000 = 1.08 x 10⁴ kgm^-3.

Question 2.
Differentiate between density and relative density.
Answer:

Density	Relative density
1. It is equal to the mass per unit volume of a body.	1. It is the ratio of density of a body to the density of water.
2. Its unit is SI kgm-3.	2. It has no unit as it is the ratio of same quantity.

 Question 3.
Arpita was given a solid sphere of metal of mass 100 g. She immersed it in a measuring cylinder and found that the level of water was raised by 30 mL. Calculate the density of metal as measured by her.
Answer:
Mass of solid = 100 g
Volume of solid=30 mL
Density of solid = \(\frac { Mass\quad of\quad Solid }{ Volume\quad of\quad Solid } =\frac { M }{ V } =\frac { 100 }{ 30 }\) = 3.33 gmL^-1

Question 4.
In the experiment, to determine the density of a given solid (denser than water) by using a spring balance and a measuring cylinder, a student made the following observations.

• Mass of solid = 115 g
• Initial reading of water level in measuring cylinder = 45 mL
• Final reading of water level in measuring cylinder = 69 mL

On the basis of these observations, what should be the density of a given solid if the spring balance showed a reading of -5 g before suspending the solid?
Answer:
Corrected mass of the solid = 115 – (-5) = 120 g
Density of solid = \(\frac { Mass\quad of\quad Solid }{ Volume\quad of\quad Solid } =\frac { M }{ V } =\frac { 120\quad g }{ \left( 69-45 \right) mL } =\frac { 120\quad g }{ 24\quad mL }\) =5 gmL^-1

Question 5.
The density of aluminium is 2700 kgm^-3. What does it mean? Calculate the density of aluminium 1 in CGS system.
Answer:
It means that 1 m³ volume of aluminium has a mass of 2700 kg.
Density of aluminium in CGS system
= \(\frac { 2700\times 1000 }{ 100\times 100\times 100 }\)
= 2700 x 10^-3
= 2.7 g cm^-3

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