# Units and Graphs

Chapters

- ap-scert-9th-class-Physical-Science-Lesson-1-Motion
- ap-scert-9th-class-Physical-Science-Lesson-2-Laws-of-Motion
- ap-scert-9th-class-Physical-Science-Lesson-3-Is-Matter-Pure?
- ap-scert-9th-class-Physical-Science-Lesson-4-Atoms-and-Molecules
- ap-scert-9th-class-Physical-Science-Lesson-5-What-is-inside-the-Atom?
- ap-scert-9th-class-Physical-Science-Lesson-6-Chemical-Reactions-and-Equations
- ap-scert-9th-class-Physical-Science-Lesson-7-Reflection-of-Light-at-Curved-Surfaces
- ap-scert-9th-class-Physical-Science-Lesson-8-Gravitation
- ap-scert-9th-class-Physical-Science-Lesson-9-Floating-Bodies
- ap-scert-9th-class-Physical-Science-Lesson-10-Work-and-Energy
- ap-scert-9th-class-Physical-Science-Lesson-11-Sound
- ap-scert-9th-class-Physical-Science-Lesson-12-Units-and-Graphs

- ap-scert-9th-class-Physical-Science-Lesson-1-Motion
- ap-scert-9th-class-Physical-Science-Lesson-2-Laws-of-Motion
- ap-scert-9th-class-Physical-Science-Lesson-3-Is-Matter-Pure?
- ap-scert-9th-class-Physical-Science-Lesson-4-Atoms-and-Molecules
- ap-scert-9th-class-Physical-Science-Lesson-5-What-is-inside-the-Atom?
- ap-scert-9th-class-Physical-Science-Lesson-6-Chemical-Reactions-and-Equations
- ap-scert-9th-class-Physical-Science-Lesson-7-Reflection-of-Light-at-Curved-Surfaces
- ap-scert-9th-class-Physical-Science-Lesson-8-Gravitation
- ap-scert-9th-class-Physical-Science-Lesson-9-Floating-Bodies
- ap-scert-9th-class-Physical-Science-Lesson-10-Work-and-Energy
- ap-scert-9th-class-Physical-Science-Lesson-11-Sound
- ap-scert-9th-class-Physical-Science-Lesson-12-Units-and-Graphs

- Solutions
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Solutions

What is Unit?

Answer:

A unit is a standard measure used for comparing measurements.

Why do we use different units for different items?

Answer:

Depending on the quantities of material the units may be expressed.

Write fundamental quantities in MKS system.

Answer:

Mass (m), Length (l) and Time (t).

What are fundamental quantities?

Answer:

Fundamental quantities are those physical quantities that cannot be expressed in terms of other quantities.

What is fundamental unit?

Answer:

Units used to express fundamental quantities are called fundamental units.

Write fundamental units in MKS system.

Answer:

Meter, Kilogram and Second.

What is CGS system?

Answer:

Centimeter, Grams and Seconds.

What is SI system? When was it introduced?

Answer:

SI system means International System of units. It was introduced in 1971.

List the fundamental quantities that are added to SI system.

Answer:

Electricity, light intensity, quantity of substance, temperature and plane angle.

What is difference between MKS and SI systems?

Answer:

- MKS system has only three fundamental quantities. Those are length, mass and time.
- SI system has eight fundamental quantities. Those are length, mass, time, electricity, light intensity, quantity of substance, temperature, plane angle.

What is derived quantity?

Answer:

The quantities that are obtained by combining fundamental quantities either by multiplication or division or both operations are called derived quantities.

What are derived units?

Answer:

The derived units of measurement derived from the fundamental units.

Write derived units of area and volume.

Derived units of area = m^{2}

Derived units of volume = m^{sup3}

What are the fundamental units are used to express the units of Force?

Answer:

Hence fundamental units used to express force are kg, m, s.

Which conversion factor is used to convert kilometers into meter?

Answer:

1000.

Which conversion factor is used to convert meters into kilometers?

Answer:

10^{-3}.

Write conversion factor to convert km/hr into m/s.

Answer:

518

Write some units of measurements expressed in the name of scientists.

Answer:

Newton (N), Pascal (Pa), Joule (J), Watt (W), etc.

What is graph?

Answer:

A pictorial form of representation that shows the relation between two quantities can be called a graph.

What are independent and dependent variables?

Answer:

Independent variables are controlled by us. Whereas dependent variables are changed due to the change in dependent variable.

Which variable is taken on x - axis?

Answer:

Independent variable.

What are grids on graph paper?

Answer:

On a graph paper, there are thick as well as fine vertical and horizontal lines. These intersecting lines form squares or grids.

What is Range?

Answer:

Range = highest value - lowest value.

What is scaling?

Answer:

Pointing of the values in the table on x - axis and y - axis is called scaling.

What is scale?

Answer:

The interval taken pointing values on axis is called scale.

How do you find x - axis scale?

Answer:

What is curved line graph?

Answer:

If a graph is in curved shape, then it is curved line graph.

What is Hooke’s law?

Answer:

The elongation of the spring is proportional to the applied mass within the elastic limit of the spring.

What is slope of the straight line graph?

Answer:

What is slope of a graph?

Answer:

The tan value of the angle at x - axis is the slope of a graph.

tan θ = Δy/Δx

What is area of a graph?

Answer:

The product of the physical quantity of y - axis and x - axis may explain another physical quantity. Hence, it is said to be area of the graph.

What does slope indicate to the graph of displacement and time?

Answer:

Velocity.

What does area of the graph of acceleration Vs time indicate?

Answer:

Predict shape of the graph if you plot a graph by taking time on x - axis and velocity of a free fall body on y - axis.

Answer:

Straight line.

Guess the shape of the graph if you plot a graph of time and distance covered by a bus.

Answer:

Curved graph.

Rithvik wrote ‘3 kgs of sugar’ on the black board. Correct him by asking a question.

Answer:

Is it correct to mention kg in plural form while writing units?

Karthik got a doubt by seeing ‘3 newtons’ on the black board. What would be it?

Answer:

Which quantity is measured in newtons ?

What are the materials / apparatus required to prove Hooke’s law?

Answer:

- Spring,
- Weights,
- Scale,
- Stand.

Area, volume, density, mass

a) Write any one fundamental quantity from the above data.

b) Write any one derived quantity from the above data.

Answer:

a) mass.

b) volume.

‘Dheeraj counted distance travelled by him for every 10 min.’

From the above data write independent and dependent variables.

Answer:

Time (min) is independent variable distance is dependent variable.

Plot the data points (6, 4) and (0, 0) in the above graph.

Answer:

How do you remember scientists through units of measurements?

Answer:

Some units are expressed in the names of the scientists like newton, joule, etc. When we use these units, scientists are remember once again.

What is the use of graph?

Answer:

- We can solve so many problems by using graphs.
- We can know the relation between two physical quantities through graphs.

Calculate the Range of 5, 7, 3, 8, 18, 4, 2, 6.

Answer:

Range = highest value – lowest value

= 18-2 = 16.

If the range is 10 and no. of grids horizontally is 20. How can you take scale X-axis?

Answer:

2) I will take 0.5,1,1.5, 2, 2.5,3,3.5, 4, 4.5, 10 on the X-axis. As a scale on x-axis.

How slope of displacement Vs time graph is useful?

Answer:

We can calculate velocity by calculating slope of line in displacement Vs time graph.

How area of velocity Vs time graph is useful?

Answer:

Area of velocity Vs time graph is useful to find the position of the object.

Answer:

Acceleration is 1 m/s^{2}.

Find the acceleration at ‘A’.

Answer:

How much distance is travelled by the object from A to B in the graph?

Answer:

Zero.

What is a unit? Where it be placed?

Answer:

- A unit is a standard measure used for comparing measurements.
- Unit should be placed right side of the magnitude of every physical quantity. For eg : 2 kg, 7 m.

Differentiate fundamental quantities and derived quantities.

Answer:

Fundamental quantity | Derived quantity |

1) Fundamental quantities are those physical quantities that cannot be expressed in terms of other quantities. | 1) The quantities that are obtained by combining fundamental quantities either by multiplication or division or both are called derived quantities. |

2) These are independent. | 2) These are dependent. |

3) Eg : Mass, length, time. | 3) Eg : Area, density, force. |

Derive units of density.

Answer:

Write different system of measurements.

Answer:

- FPS : Foot, Pound, Second.
- CGS : Centimeter, Gram, Second.
- MKS : Meter, Kilogram, Second.
- SI : Meter, Kilogram, Second, Ampere, Candela, Mole, Kelvin, Radian.

Derive units to the given physical quantities.

Answer:

Which of the following are correct? Why?

Answer:

A) m/s

B) m/s/s

C) m-s^{2}

D) 10.kgs

E) Pascal

F) joule

Answer:

A) and F) only are correct

B) two solidus are used - wrong.

C) line break is used - wrong.

D) ‘•’ and plural of kg are used - wrong.

E) capital letter used (P) - wrong.

Write correct form of units in the following.

(j) DB

(ii) mhz

(iii) 20 - m

(iv) kg.m-s^{-2}

Answer:

(i) dB

(ii) MHz

(iii) 20 m

(iv) Kg.m.s^{-2}

How do you expect the shape of the given graphs?

(a) a ∝ b

(b) a ∝ 1/b

Answer:

a) It may be straight line graph.

b) It may be curved line graph.

From the graph,

a) What is indicated by slopes of the lines OA, OB, OC?

b) Which line shows high speed than other lines? Why?

Answer:

a) Slopes of the lines indicate speeds of the objects.

b) OA shows high speed than other lines.

Because it has high slope than others.

a) Which is independent variable?

b) Which is dependent variable?

c) Predict how the graph is.

d) Find the range on Y - axis.

Answer:

a) Mass

b) Weight

c) It may be in straight line.

d) On Y - axis, values are 98, 196, 294, 392, 490.

Range = 490 - 98 = 392

Plot the given data points on the given graph paper and join the dots.

Data points : (8, 10) (20, 15) (40, 22.5) (48, 0)

Answer:

Draw a graph roughly to show uniform velocity of a body.

Answer:

Draw a graph that shows a body without movement after travelling sometime.

Answer:

How do you appreciate the role of graphs in solving problems?

Answer:

- Graphs can be used to compare different physical quantities like time- displacement, time-velocity, pressure-volume, etc. and helps in solve the problems.
- Graphs are very useful to find the path of an object which is in motion and it is easy to calculate velocity, acceleration, position, etc. at particular time and particular point of the object.
- Graphs are very useful minimum, maximum values of some physical quantities. For example to find minimum deviation of a prism graphs are very useful.
- In this way graphs are appreciable for their role in solving problems.

From the given graph find the slope and area at point B.

Answer:

Convert 3 m/s into km/hr.

Answer:

A ball of 100 g mass is thrown with initial velocity of 0.01 km/s. What is its momentum at that time?

Answer:

Momentum = mass × velocity

Here, mass of the ball = 100 gr = 100 × 1/100 kg ⇒ m = 0.1 kg

Velocity of the ball = 0.01 km/s = 0.01 × 1000 m/s ⇒ v = 10 m/s

Momentum of the ball = mxv = 0.1 × 10 kg.m/s = 1 kg.m/s

Find the temperature on Day - 4 by using graph.

Answer:

From the graph the temperature on day - 4 is 43°C.

Observe table and answer the following.

i) 12 cm = …………. m

ii) 2 nm = …………. cm

Answer:

i) 12 cm = 12 × 10^{-2}m

ii) 2 nm = 2 × 10^{-7}cm

[From the table 1 nanometer = 10_{-9}m; 1 centimeter = 10^{-2}m.

1 nanometer to centimeter conversion factor = 10^{-9-(-2)}= 10^{-7}.]

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