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Motion and Measurement of Distances - Measurement of Length and Curvy Lines

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

Standard Units of Measurement: In ancient times, people used handspans, cubits, or foot lengths, but these varied from person to person. To maintain uniformity, the International System of Units (SI units) was adopted. The SI unit of length is the metremetre (mm).

Measuring Length Correctly: The scale should be placed in contact with the object along its length. If the zero mark is broken or not clear, any other full mark (like 1.0 cm1.0 \text{ cm}) can be used as the starting point.

Parallax Error: To get an accurate reading, the eye must be placed exactly vertically above the point where the measurement is to be taken. Looking from an angle leads to errors.

Measuring Curved Lines: A straight ruler cannot measure a curved path directly. A thread is used to trace the curved line from one end to the other. The length of the thread is then measured using a standard scale.

Unit Hierarchy: For very long distances, we use kilometreskilometres (kmkm). For small lengths, we use centimetrescentimetres (cmcm) or millimetresmillimetres (mmmm).

📐Formulae

1 km=1000 m1 \text{ km} = 1000 \text{ m}

1 m=100 cm1 \text{ m} = 100 \text{ cm}

1 cm=10 mm1 \text{ cm} = 10 \text{ mm}

Actual Length=Reading at the second endReading at the first end\text{Actual Length} = \text{Reading at the second end} - \text{Reading at the first end}

💡Examples

Problem 1:

The distance between two points on a curved line measured using a thread is found to correspond to the distance between the 2.5 cm2.5 \text{ cm} mark and the 18.7 cm18.7 \text{ cm} mark on a ruler. What is the length of the curved line?

Solution:

Length =18.7 cm2.5 cm=16.2 cm= 18.7 \text{ cm} - 2.5 \text{ cm} = 16.2 \text{ cm}

Explanation:

When the zero mark is not used, the actual length is the difference between the final reading and the initial reading on the scale.

Problem 2:

Convert a distance of 5.45 km5.45 \text{ km} into metresmetres and centimetrescentimetres.

Solution:

In metres: 5.45×1000=5450 m5.45 \times 1000 = 5450 \text{ m}. In centimetres: 5450×100=5,45,000 cm5450 \times 100 = 5,45,000 \text{ cm}.

Explanation:

Since 1 km=1000 m1 \text{ km} = 1000 \text{ m}, we multiply by 10001000 to convert to metres. Then, since 1 m=100 cm1 \text{ m} = 100 \text{ cm}, we multiply the result by 100100.