Measurement of Length and MotionClass 6 Science NCERT Solutions
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Q1Let us enhance our learning
Some lengths are given in Column I of Table 5.5. Some units are given in Column II. Match the lengths with the units suitable for measuring those lengths.
Table 5.5
Column I Column II Distance between Delhi and Lucknow centimetre Thickness of a coin kilometre Length of an eraser metre Length of school ground millimetre
Solution
Here is the matching of lengths with suitable units:
- Distance between Delhi and Lucknow: This is a very large distance, so
kilometreis the most suitable unit. - Thickness of a coin: This is a very small length, so
millimetreis the most suitable unit. - Length of an eraser: This is a small object, so
centimetreis the most suitable unit. - Length of school ground: This is a moderate to large length, so
metreis the most suitable unit.
Matched Table:
| Column I | Column II |
|---|---|
| Distance between Delhi and Lucknow | kilometre |
| Thickness of a coin | millimetre |
| Length of an eraser | centimetre |
| Length of school ground | metre |
Q2Let us enhance our learning
Read the following statements and mark True (T) or False (F) against each.
(i)
The motion of a car moving on a straight road is an example of linear motion.
(ii)
Any object which is changing its position with respect to a reference point with time is said to be in motion.
(iii)
Solution
(i)
True (T)
Linear motion is defined as the motion of an object along a straight line. A car moving on a straight road follows a straight path, hence it is an example of linear motion.
(ii)
True (T)
An object is considered to be in motion if its position changes over time relative to a fixed reference point. If its position does not change, it is considered at rest.
(iii)
False (F)
Let us check the conversion:
We know that .
And .
Therefore, .
The statement is incorrect.
Q3Let us enhance our learning
Which of the following is not a standard unit of measuring length? (i) millimetre (ii) centimetre (iii) kilometre (iv) handspan
Solution
The correct option is (iv) handspan.
Explanation:
Standard units of measurement are those that are universally accepted and provide consistent results regardless of who is performing the measurement. Millimetre (mm), centimetre (cm), and kilometre (km) are all standard units of length within the International System of Units (SI units).
A handspan, however, is a non-standard unit of measurement. Its length varies from person to person, making measurements inconsistent and unreliable for universal use. Ancient Indian literature mentions units like 'angula' (finger width) and 'balisht' (handspan), but these are not considered standard units in modern scientific measurements due to their variability.
Q4Let us enhance our learning
Search for the different scales or measuring tapes at your home and school. Find out the smallest value that can be measured using each of these scales. Record your observations in a tabular form.
Solution
This is an activity-based question. To find the smallest value that can be measured using a scale or measuring tape, you need to look at the smallest divisions marked on it. The smallest division represents the least count of the measuring instrument.
For example, on a typical scale (like the one shown in Fig. 5.3 in the textbook):
Procedure:
- Examine the scale carefully.
- Identify the main markings (e.g.,
cm). - Observe the smaller divisions between consecutive main markings.
- On many standard scales, each
centimetre(cm) is further divided into equal smaller parts. - The length of one of these smaller parts is called a
millimetre(mm).
Observation for a standard scale:
- Smallest value: ()
Example of a tabular form for recording observations:
| Measuring Device | Smallest Value (Least Count) |
|---|---|
| ruler | |
| Metre scale | |
| Tailor's tape | |
| Measuring tape (for construction) | or (depending on markings) |
Q5Let us enhance our learning
Suppose the distance between your school and home is . Express it in metres.
Solution
Given:
Distance between school and home
To Find:
Distance in metres
Formula:
We know the conversion factor between kilometres and metres:
Calculation:
To convert the distance from kilometres to metres, we multiply the value in kilometres by .
Final Answer:
The distance between the school and home is .
Q6Let us enhance our learning
Take a tumbler or a bottle. Measure the length of the curved part of the base of glass or bottle and record it.
Solution
This is an activity-based question. To measure the length of a curved part, such as the base of a glass or bottle, a flexible measuring tool is required. The textbook suggests using a thread for this purpose.
Procedure:
- Take a piece of thread. The thread should be long enough to go around the curved base of the tumbler or bottle.
- Place one end of the thread at a specific point on the curved base.
- Carefully wrap the thread along the curved path of the base, keeping it taut and in contact with the surface.
- Mark the point on the thread where it meets the starting point after completing one full circle around the base.
- Straighten the thread.
- Measure the length of the thread between the starting point and the marked point using a standard metre scale or a scale.
- Record this measured length.
(Refer to Fig. 5.8 in the textbook for an illustration of measuring a curved line with a thread.)
Q7Let us enhance our learning
Measure the height of your friend and express it in (i) metres (ii) centimetres and (iii) millimetres.
Solution
This is an activity-based question that involves measurement and unit conversion.
Procedure:
- Ask your friend to stand straight against a wall. Ensure their heels are touching the wall and their head is erect.
- Use a metre scale or a measuring tape to measure their height from the floor to the top of their head. An adult can help by placing a flat object (like a book) horizontally on the friend's head and marking the point on the wall.
- Read the measurement from the scale. Let's assume a hypothetical measurement for demonstration.
Hypothetical Measurement Example:
Let's say the height of your friend is .
Conversions:
(i)
Expressing height in metres (m):
We know that .
To convert centimetres to metres, divide by .
(ii)
Expressing height in centimetres (cm):
This is our initial measurement.
Height
(iii)
Expressing height in millimetres (mm):
We know that .
To convert centimetres to millimetres, multiply by .
Final Answer (based on hypothetical example):
If the height of the friend is , then:
(i)
In metres:
(ii)
In centimetres:
(iii)
In millimetres:
Q8Let us enhance our learning
You are given a coin. Estimate how many coins are required to be placed one after the other lengthwise, without leaving any gap between them, to cover the whole length of the chosen side of a notebook. Verify your estimate by measuring the same side of the notebook and the size of the coin using a scale.
Solution
This is an activity-based question that involves estimation and verification through actual measurement.
Procedure:
1. Estimation:
- Take a coin (e.g., a coin) and place it along one side of your notebook.
- Visually estimate how many such coins would be needed to cover the entire length of that side without any gaps. Make a rough guess.
- Example Estimation: If the notebook side looks like it is about and a coin is about in diameter, you might estimate coins.
2. Verification by Measurement:
- Measure the length of the chosen side of the notebook: Use a scale to accurately measure the length of the side of the notebook. If the notebook is longer than , measure it in parts or use a longer scale.
- Example Measurement: Let the length of the notebook side be .
- Measure the size (diameter) of the coin: Place the coin on the scale and measure its diameter carefully.
- Example Measurement: Let the diameter of the coin be .
- Calculate the actual number of coins needed: Divide the length of the notebook side by the diameter of one coin.
- Example Calculation: Since you cannot place a fraction of a coin, you would need full coins and a small part of a ninth coin, or practically, coins if you need to cover the entire length (with a slight overlap or gap).
3. Comparison:
Compare your initial estimate with the calculated number of coins. Discuss any differences and the reasons for them (e.g., visual distortion, imprecise estimation).
This activity helps in understanding the importance of accurate measurement over mere estimation.
Q9Let us enhance our learning
Give two examples each for linear, circular and oscillatory motion.
Solution
Here are two examples for each type of motion, as discussed in the chapter:
-
Linear Motion: When an object moves along a straight line.
- A car moving on a straight road.
- The march-past of students during a parade.
- An object (like an eraser or an orange) dropping straight down from a height.
-
Circular Motion: When an object moves along a circular path.
- A child playing on a merry-go-round.
- Whirling an eraser (or a potato) tied to a thread in a circle.
-
Oscillatory Motion: When an object moves to and fro (back and forth) about some fixed position.
- The motion of a swing.
- The motion of a pendulum in a clock.
- The vibrating motion of a metal strip fixed at one end.
Q10Let us enhance our learning
Observe different objects around you. It is easier to express the lengths of some objects in mm, some in cm and some in m. Make a list of three objects in each category and enter them in the Table 5.6.
Table 5.6: Sizes of objects around us
Size
mm
m
Solution
This is an activity-based question. The choice of unit depends on the typical size of the object being measured for convenience and clarity. Here are examples for each category:
Table 5.6: Sizes of objects around us
| Unit (Size) | Object 1 | Object 2 | Object 3 |
|---|---|---|---|
mm | Thickness of a coin | Thickness of a page | Length of an ant |
cm | Length of a pencil | Width of a book | Length of an eraser |
m | Height of a door | Length of a room | Length of a school ground |
Q11Let us enhance our learning
A rollercoaster track is made in the shape shown in Fig. 5.19. A ball starts from point A and escapes through point F. Identify the types of motion of the ball on the rollercoaster and corresponding portions of the track.
Solution
Based on the typical design of a rollercoaster track (as implied by Fig. 5.19, which usually features straight sections, curves, and loops), we can identify the following types of motion for the ball:
-
Linear Motion: This occurs when the ball moves along a straight path.
- Corresponding portions: Straight sections of the track, such as the initial descent from point A (e.g., A to B), or any flat or inclined straight segments (e.g., D to E).
-
Circular Motion: This occurs when the ball moves along a curved path or a loop.
- Corresponding portions: The sections of the track that form loops (e.g., B-C-D if it's a loop) or sharp turns and curves (e.g., E to F, or any other curved segment).
Note: While oscillatory motion involves a 'to and fro' movement around a fixed point, it is generally not the primary motion on a continuous rollercoaster track designed for forward movement. The dominant motions would be linear and circular/curvilinear.
Q12Let us enhance our learning
Tasneem wants to make a metre scale by herself. She considers the following materials for it-plywood, paper, cloth, stretchable rubber and steel. Which of these should she not use and why?
Solution
Tasneem should not use paper, cloth, and stretchable rubber for making a metre scale.
Reasons:
- Paper: Paper can easily bend, tear, or get crumpled. It can also absorb moisture, which might cause it to expand or contract. These properties make it unsuitable for precise and consistent length measurements.
- Cloth: Cloth is a flexible material and can stretch or shrink. Its length can change significantly when pulled or due to environmental factors like humidity. A scale made of cloth would not provide accurate or reproducible measurements.
- Stretchable rubber: As the name suggests, stretchable rubber can be easily stretched. If a scale is made from rubber, its length would vary depending on how much it is stretched, leading to highly inaccurate measurements.
Suitable Materials:
Plywood and steel are suitable materials because they are rigid and do not easily change their length or shape under normal conditions, ensuring consistent and accurate measurements.
Q13Let us enhance our learning
Think, design and develop a card game on conversion of units of length to play with your friends.
Solution
This is a design and development activity. Here is an idea for a card game on conversion of units of length:
Game Title: Unit Conversion Challenge
Objective: To be the first player to correctly match or convert units of length.
Materials: A deck of cards. Each card will have a length written on it in a specific unit.
Examples of Cards:
- Card 1: ""
- Card 2: ""
- Card 3: ""
- Card 4: ""
- Card 5: ""
- Card 6: ""
- Card 7: ""
- Card 8: ""
How to Play (Example Rules - 'Matching Game'):
- Setup: Shuffle the cards and deal them face down in a grid on a table.
- Turns: Players take turns flipping over two cards.
- Matching: If the two cards represent the same length (e.g., "" and "" or "" and ""), the player keeps the pair and gets another turn.
- No Match: If the cards do not match, the player flips them back face down, and the turn passes to the next player.
- Winning: The game continues until all pairs have been found. The player with the most pairs wins.
Variations (for advanced play - 'Conversion Race'):
- Each player is dealt a hand of cards with different lengths (e.g., "", "", "", etc.).
- A 'target unit' card (e.g., "Convert to
metres") is drawn from a separate deck. - Players must quickly convert all their cards to the target unit. The first player to correctly state the converted values for all their cards wins the round.
This game encourages quick recall of unit conversions and reinforces the understanding of standard units of length.