Key Concept: Definition

c) The first section providing context and stating the purpose
[Solution Description]
An introduction is the first section of a paper that provides context, introduces the topic, and states the thesis or purpose of the work.

Key Concept: Basic Concept

c) To present background information and outline main points
[Solution Description]
The primary purpose of an introduction is to provide background information and outline the main points that will be discussed. It sets the stage for the reader.

Key Concept: General

a) Cannot generate due to empty syllabus
[Solution Description]

Key Concept: Handspan measurement, Unit comparison

b) 1090 mm
[Solution Description]
First, calculate Deepa's measurement:
$6 \text{ handspans} \times 18 \text{ cm/handspan} = 108 \text{ cm}$.
Then, calculate Tasneem's measurement:
$5 \text{ handspans} \times 22 \text{ cm/handspan} = 110 \text{ cm}$.
Average both measurements for better accuracy:
$(108 + 110)/2 = 109 \text{ cm}$.
Convert to millimeters:
$109 \text{ cm} \times 10 \text{ mm/cm} = 1090 \text{ mm}$.

Key Concept: Traditional Methods of Measurement

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The syllabus mentions that measuring length using body parts like handspan is a traditional method, which makes Assertion (A) true. The Reason (R) states that different people may have different handspans, leading to variations in measurements. This is also true and directly explains why traditional methods like handspan can lead to inconsistent results. Therefore, both Assertion and Reason are true, and Reason correctly explains the Assertion.

Key Concept: Correct Measurement Practices

b) To avoid errors caused by viewing from an angle
[Solution Description]
Placing the eye directly above the measurement point avoids parallax error, ensuring accurate readings as emphasized in the syllabus.

Key Concept: Unit Conversion

b) 38.1 cm
[Solution Description]
Multiply the length in inches by the conversion factor:
$15 \text{ inches} \times 2.54 \text{ cm/inch} = 38.1 \text{ cm}$
The length is 38.1 cm.

Key Concept: Traditional units, Conversion

a) 8.27 inches
[Solution Description]
First, convert angulas to cm: $12 \text{ angulas} \times 1.75 \text{ cm/angula} = 21 \text{ cm}$. Now, convert cm to inches: $21 \text{ cm} \div 2.54 \text{ cm/inch} \approx 8.2677 \text{ inches}$. Rounding to two decimal places, the length is 8.27 inches.

Key Concept: Traditional units of measurement, Need for standardized units

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that traditional units like angula and handspan lead to measurement inconsistencies because they vary from person to person. This is true as seen in Table 5.1 where different students measured the same table with slightly varying handspans. The reason explains why standardized units are needed—to ensure consistency in measurements across different individuals. Both statements are true, and the reason correctly explains the assertion.

Key Concept: Conversion of units, Angula to modern units

c) 7.00 cm
[Solution Description]
Given that 1 angula equals 1.75 cm, four angulas (char angula) would be $4 \times 1.75 = 7$ cm. This calculation shows the conversion from traditional units (angula) to modern metric units (cm).

Key Concept: Standard units of measurement

b) Metre ($m$)
[Solution Description]
The question asks about the standard unit of length as per the International System of Units (SI). The textbook clearly states that the SI unit of length is the metre, symbolized as $m$.

Key Concept: Ancient Indian units of measurement

c) Angula
[Solution Description]
The question refers to an ancient Indian unit of measurement mentioned in the textbook. The text specifies that the $angula$ (finger width) is still used by traditional craftspeople like carpenters and tailors.

Key Concept: Measurement using body parts

c) Different people have different sized handspans
[Solution Description]
Measuring length using body parts like handspan is not reliable because the size of body parts varies from person to person. This leads to inconsistent measurements, as seen in Table 5.1 where different students recorded slightly different handspans for the same table.

Key Concept: Correct Measurement Technique

c) Place the scale in contact with the object and view directly above its tip
[Solution Description]
To measure length correctly, place the scale in contact with the object along its length and position your eye directly above the tip of the object while reading the scale. Incorrect placement or viewing angle leads to errors.

Key Concept: Unit Definition, Measurement Components

d) "13" is the number and "handspan" is the unit
[Solution Description]
In the measurement "13 handspans," the number "13" represents the quantity (how many times the unit is counted), and "handspan" represents the unit of measurement. Together, they describe the length of the table.

Key Concept: Handspan Measurement

c) Handspan varies from person to person, leading to different measurements.
[Solution Description]
The measurements vary because handspans differ from person to person. Anish's measurement is 13.5 handspans, Padma's is 13, Tasneem's is 12.5, Deepa's is 13.5, and Hardeep's is 14. This variation indicates that handspan is not a consistent unit.

Key Concept: Measuring with body parts, Consistency in measurement

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion claims that using handspan ensures consistency, but the syllabus clearly states that handspan measurements vary due to differences in individual hand sizes. For example, Table 5.1 shows students reporting different measurements for the same table when using their handspans. Therefore, the assertion is false because handspan-based measurements are not consistent. However, the reason correctly explains why inconsistency arises—because the size of a handspan differs among individuals. Thus, while the assertion is false, the reason is true.

Key Concept: Non-Standard Units, Multiple Measurements

c) 0.68m to 0.96m
[Solution Description]
Given Bina's measurement: 180 strides = 0.8m per stride
So corridor length = 180 × 0.8 = 144m
Now find others' stride lengths relative to Bina:
Arjun took fewer strides → his stride > Bina's
Chetan took more strides → his stride < Bina's
Arjun's stride = $\frac{144}{150}$ = 0.96m
Chetan's stride = $\frac{144}{210}$ ≈ 0.6857m
Range is from shortest stride to longest: 0.6857m to 0.96m

Key Concept: Measurement components

c) As both number and unit
[Solution Description]
Length is expressed in two parts: a number representing how many units, and the unit itself (e.g., 13 handspans). Both components are necessary to properly describe a measurement.

Key Concept: Need for standard units

d) Standard units provide consistent and uniform measurements.
[Solution Description]
Non-standard units such as handspans differ from person to person, leading to inconsistent measurements of the same object. Standard units ensure uniformity and consistency in measurements regardless of who performs the measurement. This eliminates ambiguity and allows for reliable comparison of measurements.

Key Concept: Standard vs. non-standard units, Consistency

c) Standard units eliminate variability caused by personal differences.
[Solution Description]
Handspans vary from person to person, leading to inconsistent measurements, whereas a meter scale provides a universally accepted standard. Standard units ensure repeatability and comparability of measurements regardless of who performs them.

Key Concept: Conversion of Units

b) 500 cm
[Solution Description]
The conversion factor between metres and centimetres is $1 \text{ m} = 100 \text{ cm}$. Therefore, to convert 5 metres to centimetres:
$5 \text{ m} = 5 \times 100 \text{ cm} = 500 \text{ cm}$
The correct equivalent length is 500 cm.

Key Concept: Need for standard units

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that using handspans as a unit leads to inconsistent results. This is true because different people have different handspan sizes, leading to varying measurements for the same object. The reason explains why this inconsistency occurs—because handspan sizes differ among individuals. Hence, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Standard Units

b) Metre
[Solution Description]
The International System of Units (SI) defines the standard unit for length as metre, symbolized by 'm'. This is universally accepted to maintain consistency in measurements across different regions and applications.

Key Concept: Unit Conversion

b) 3500 mm
[Solution Description]
To convert meters to millimeters, we use the conversion factors: $1 m = 100 cm$ and $1 cm = 10 mm$.
Step 1: Convert meters to centimeters:
$3.5 m = 3.5 \times 100 cm = 350 cm$
Step 2: Convert centimeters to millimeters:
$350 cm = 350 \times 10 mm = 3500 mm$
Therefore, the length of the rope is 3500 mm.

Key Concept: Unit Conversion, Multi-step Calculation

a) 45000000 mm
[Solution Description]
First, convert kilometers to meters using $1 km = 1000 m$. So, $45 km = 45000 m$. Next, convert meters to centimeters using $1 m = 100 cm$, so $45000 m = 4500000 cm$. Finally, convert centimeters to millimeters using $1 cm = 10 mm$, so $4500000 cm = 45000000 mm$.

Key Concept: Unit Conversion

d) 10
[Solution Description]
According to the SI system, $1 \text{ cm} = 10 \text{ mm}$. This conversion comes directly from the standard definitions.

Key Concept: Mixed Unit Conversion, Conceptual Understanding

a) 3.66 m
[Solution Description]
First, convert feet to inches:
12 feet = $12 \times 12$ inches = 144 inches
Next, convert inches to centimeters using the given conversion factor:
144 inches = $144 \times 2.54$ cm = 365.76 cm
Finally, convert centimeters to meters:
365.76 cm = 365.76 / 100 m = 3.6576 m
Hence, the length of the plank is approximately 3.66 meters when rounded to two decimal places.

Key Concept: Writing SI units correctly

c) km
[Solution Description]
The symbol for kilometre should always be written in lowercase letters as $km$. It should not have a full stop or an 's' for plural.

Key Concept: SI units, Conversion between units

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
First, evaluate Assertion (A): The statement claims that the conversion factor from kilometres to millimetres is $10^6$.
- By definition, $1 \text{ km} = 1000 \text{ m}$ (kilo- prefix = $10^3$).
- Also, $1 \text{ m} = 1000 \text{ mm}$ (milli- prefix = $10^{-3}$, so $1 \text{ m} = \frac{1}{10^{-3}} \text{ mm} = 10^3 \text{ mm}$).
- Thus, $1 \text{ km} = 1000 \text{ m} \times 1000 \text{ mm/m} = 10^6 \text{ mm}$.
Next, evaluate Reason (R): It states that the SI prefixes kilo- and milli- represent $10^3$ and $10^{-3}$ respectively, leading to a combined conversion factor of $10^6$.
- This is correct because when converting from km to mm, you multiply by $10^3$ (kilo-) and then divide by $10^{-3}$ (milli-), equivalent to multiplying by $10^6$.
Conclusion: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Key Concept: Unit Conversion

b) 250 mm
[Solution Description]
To convert centimeters to millimeters, use the conversion factor $1\ cm = 10\ mm$. Multiply the given length by this factor:
$25\ cm \times 10\ \frac{mm}{cm} = 250\ mm$

Key Concept: Symbol usage

d) m
[Solution Description]
According to the SI system, the symbol for meter is always written in lowercase 'm'. It should not be capitalized unless it starts a sentence, and it should never be followed by an 's' or a full stop (unless at the end of a sentence).

Key Concept: Multi-Step Conversion, Conceptual Complexity

a) 5200 m
[Solution Description]
Convert kilometers to meters: $5.2$ km $\times 1000$ m/km $= 5200$ m.
Now, consider the remaining $0.2$ km: $0.2$ km $\times 1000$ m/km $= 200$ m.
For centimeters, $5200$ m is already in meters, but we can also express $200$ m as $200 \times 100$ cm $= 20000$ cm.
However, the question asks for meters and centimeters combined, so the total length is $5200$ m (since $200$ m is included in $5200$ m).
Alternatively, if interpreted as sum: $5200$ m + $20000$ cm $= 5400$ m (but this leads to inconsistency). The correct interpretation is $5200$ m only.

Key Concept: Unit Conversion and Addition

a) 370 cm
[Solution Description]
First, convert millimetres to centimetres using the relation $1 \text{ cm} = 10 \text{ mm}$. Thus, $1200 \text{ mm} = \frac{1200}{10} = 120 \text{ cm}$. Now add the two lengths:
$250 \text{ cm} + 120 \text{ cm} = 370 \text{ cm}$.

Key Concept: Distance calculation, unit conversion

c) 25201
[Solution Description]
First, convert the total length from kilometres to centimetres: $12.6 \text{ km} = 12.6 \times 1000 \text{ m} = 12600 \text{ m}$, then $12600 \times 100 = 1260000 \text{ cm}$. The interval between sleepers is 50 cm. Since the first sleeper starts at 0 cm, the number of sleepers is $\dfrac{1260000}{50} + 1 = 25200 + 1 = 25201$.

Key Concept: Unit Conversion

c) 3500 m
[Solution Description]
To convert kilometres to metres, we know that $1 \text{ km} = 1000 \text{ m}$. Therefore, multiply the given value by 1000:
$3.5 \text{ km} \times 1000 = 3500 \text{ m}$.

Key Concept: Metric and Non-metric Units

c) Assertion is true, but Reason is false.
[Solution Description]
The Assertion states that the foot is a non-metric unit of length commonly used in the United States. This is true because the foot is not part of the metric system but is part of the imperial system, which is primarily used in the United States. The Reason claims that the foot is part of the SI system and widely adopted worldwide, which is false. The SI unit for length is the meter, not the foot. Therefore, Assertion is true, but Reason is false.

Key Concept: Conversion between metric and non-metric units

b) 182.88 cm
[Solution Description]
We know that $1$ foot = $12$ inches and $1$ inch = $2.54$ cm. First, convert feet to inches: $6$ feet $\times 12$ inches/foot = $72$ inches. Then, convert inches to centimetres: $72$ inches $\times 2.54$ cm/inch = $182.88$ cm. Therefore, the approximate length of the wooden plank in centimetres is $182.88$ cm.

Key Concept: Metric and non-metric conversion, multi-step calculation

c) 104.14 cm
[Solution Description]
Step 1: Convert feet to inches. Given that 1 foot = 12 inches, so 3 feet = $3 \times 12 = 36$ inches.
Step 2: Add the remaining inches. Total length in inches = $36 + 5 = 41$ inches.
Step 3: Convert inches to centimeters. Since $1 \text{ inch} = 2.54 \text{ cm}$, total length in cm = $41 \times 2.54 = 104.14$ cm.

Key Concept: Measuring Length with Broken Scale

b) 7.4 cm
[Solution Description]
When the zero mark of the scale is broken, we must subtract the initial reading from the final reading to get the correct length. Here, the initial reading is 5.3 cm and the final reading is 12.7 cm. So, the length is $12.7 \text{ cm} - 5.3 \text{ cm} = 7.4 \text{ cm}$.

Key Concept: Eye Position While Measuring

c) To avoid parallax error and get an accurate reading
[Solution Description]
Keeping the eye directly above the tip of the object ensures that the measurement is taken perpendicular to the scale, avoiding parallax error. This gives an accurate reading as the line of sight is straight and not at an angle, which could otherwise cause incorrect measurements.

Key Concept: Eye position, Scale placement

d) Both under- and overestimation are possible depending on the angle
[Solution Description]
Observing from an angle causes parallax error, leading to incorrect readings because the eye is not directly above the point being measured. This results in an apparent shift in the position of the tip.

Key Concept: Correct placement of the scale

c) Place the scale in contact with the object along its length
[Solution Description]
The correct way to place the scale is to ensure it is in direct contact with the object along its length, without any gaps or misalignment. This ensures an accurate measurement. Fig. 5.4 in the syllabus shows the correct and incorrect placements. The correct option involves placing the scale flat against the object.

Key Concept: Correct method of measuring length using a scale with broken ends

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, when the ends of a scale are broken or the zero marking is not clear, any other full mark (e.g., 1.0 cm) can be used as a reference point. The length is obtained by subtracting the first reading from the second reading (e.g., $10.4\,\text{cm} - 1.0\,\text{cm} = 9.4\,\text{cm}$). Here, both Assertion (A) and Reason (R) are true, and Reason correctly explains why this method works. It accounts for the offset caused by the broken end without needing the zero mark.

Key Concept: Correct Eye Position

b) Directly above the point being measured
[Solution Description]
The correct position of the eye while reading a measurement on a scale is directly above the point being measured to avoid parallax error.

Key Concept: Correct scale placement, Eye position

b) 11.3 cm
[Solution Description]
Since the scale does not start from zero, we subtract the initial marking (1.5 cm) from the final reading (12.8 cm). The length of the pencil is $12.8 \text{ cm} - 1.5 \text{ cm} = 11.3 \text{ cm}$. The correct positioning of the eye ensures there is no parallax error in the measurement.

Key Concept: Visually challenged measurements, Correct scale placement

a) 22.5 cm
[Solution Description]
The correct length is calculated by subtracting the initial mark from the final mark: $25.5 \text{ cm} - 3.0 \text{ cm} = 22.5 \text{ cm}$. Since the scale was placed correctly, the tactile measurement provides an accurate result without parallax error.

Key Concept: Broken Scale Measurement

c) 6.6 cm
[Solution Description]
When using a broken scale, subtract the reading at one end from the other end to get the correct length. Here, $8.9 \text{ cm} - 2.3 \text{ cm} = 6.6 \text{ cm}$.

Key Concept: Broken scale measurement, multiple steps

b) 12.0 cm
[Solution Description]
First, compute the apparent length using the broken scale: $14.8 \text{ cm} - 2.3 \text{ cm} = 12.5 \text{ cm}$. Next, account for the alignment error by subtracting the correction factor: $12.5 \text{ cm} - 0.5 \text{ cm} = 12.0 \text{ cm}$. The corrected length of the pencil is 12.0 cm.

Key Concept: Conversion of Units

c) 2.54 cm
[Solution Description]
According to the syllabus, $1 \text{ inch} = 2.54 \text{ cm}$. This is a standard conversion factor.

Key Concept: Using broken scale ends

a) 9.3 cm
[Solution Description]
The scale is broken, so we cannot directly use the initial reading. Instead, subtract the lower marking (3.5 cm) from the higher marking (12.8 cm) to get the actual length of the pencil.
Calculation: $12.8 \text{ cm} - 3.5 \text{ cm} = 9.3 \text{ cm}$. Thus, the correct length is 9.3 cm.

Key Concept: Measuring tools for visually challenged persons

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion states that visually challenged students use smooth scales with no markings, which is incorrect. According to the syllabus, they use scales with raised markings that can be felt by touching them. The reason correctly explains that scales with raised markings help visually challenged students feel the divisions and measure accurately. Therefore, the assertion is false, but the reason is true.

Key Concept: Standard Units, Measuring tools for visually challenged persons

c) Stick to one unit system and ensure the tape is snug but not tight.
[Solution Description]
To maintain consistency, the tailor must stick to one unit system (either inches or centimetres) throughout the measurement process. Mixing units can lead to confusion and incorrect measurements. Additionally, the tailor must ensure that the tape is snug but not tight around the tree to avoid compressing the bark, which could lead to an inaccurate girth measurement.

Key Concept: Measuring tools for visually challenged persons, Correct position of the eye

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
First, let us understand the assertion and reason separately. The assertion states that visually challenged students can measure lengths accurately without needing their eye directly above the object. This is true because they rely on tactile feedback from raised markings on the scale rather than visual alignment. The reason states that the correct position of the eye should be directly above the object to avoid parallax error, which is also true for sighted individuals. However, this reason does not explain the assertion since visually challenged individuals do not depend on visual alignment at all.
Therefore, both Assertion and Reason are individually true, but Reason does not explain Assertion.

Key Concept: Thread method, Measurement conversion

a) 450 mm
[Solution Description]
Since 1 centimeter (cm) equals 10 millimeters (mm), the length of the thread in millimeters is calculated as:
Length in mm = Length in cm × 10
Length in mm = 45 cm × 10 = 450 mm
Therefore, the length of the thread is 450 mm.

Key Concept: Measuring the Length of a Curved Line

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion is true because the syllabus explicitly mentions that the length of a curved line can be measured by using a thread (as shown in Fig. 5.8), which is then straightened and measured using a metre scale. The reason is also true, as a flexible thread can indeed conform to the shape of a curve, making it possible to straighten it and measure its length accurately. Moreover, the reason correctly explains why the method works, as the flexibility of the thread is essential for conforming to the curve before straightening. Thus, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Measuring maze distance

b) 15
[Solution Description]
First, calculate the total length contributed by the 2 cm lines: $5 \times 2 \, \text{cm} = 10 \, \text{cm}$. Subtract this from the total maze length to find the length contributed by the 1 cm lines: $25 \, \text{cm} - 10 \, \text{cm} = 15 \, \text{cm}$. Then, divide this by the length of each 1 cm line to get the number of such lines: $15 \, \text{cm} / 1 \, \text{cm} = 15$.

Key Concept: Flexible tape measurement, error analysis

b) The tape was stretched during measurement
[Solution Description]
Flexible tapes can stretch over time or due to excessive force during measurement. If the tape is stretched while measuring, it will show a higher length than the actual value. Here, the measured value (205 cm) is greater than the actual value (200 cm), indicating the tape was likely stretched.

Key Concept: Measuring the length of a curved line using flexible tape

d) Digital calipers
[Solution Description]
A flexible tape or thread can be used to follow the curve and then straightened to measure the length. A straight ruler cannot follow the curve, so it is unsuitable. Digital tools like calipers are typically used for small, precise linear measurements and not for large curves.

Key Concept: Measuring the Length of a Curved Line, Use of Thread or Flexible Tape

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion claims that a stretchable rubber thread can accurately measure the length of a highly irregular curved line. However, stretchable materials like rubber introduce errors because their length changes when stretched, leading to inaccurate measurements. The reason states stretchable materials provide precision due to dynamic adjustment, which is false because stretching alters the actual length. Therefore, while the reason attempts to justify the assertion, both are incorrect in the context of accurate measurement. A non-stretchable thread or flexible tape should be used for precise measurements.

Key Concept: Measuring curved lines using a thread

b) 18 cm
[Solution Description]
The length of the thread after straightening gives the exact circumference of the bangle. Thus, the circumference is equal to the straightened thread's length, which is 18 cm.

Key Concept: Method to Measure Curved Lines

b) Flexible measuring tape
[Solution Description]
To measure curved lines, flexible tools like a measuring tape or thread are used because they can bend along the curve. Once straightened, their length can be measured with a metre scale. The correct answer is "Flexible measuring tape" as it directly matches the syllabus method.

Key Concept: Measuring Curved Lines

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a thread can measure the length of a curved line accurately when a flexible tape is unavailable. This is correct as per the syllabus, which mentions using a thread placed along the curve and then measured with a scale. The reason explains why this method works—by following the exact curve—which aligns with the key point in the syllabus about ensuring accuracy by following the curve precisely. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Fixed Reference Point

b) It ensures everyone gets the same measurement.
[Solution Description]
A fixed reference point ensures consistency in measuring positions. Without it, measurements become relative to arbitrary points, leading to varying results. For example, the students' differing opinions about the garden's distance were due to no fixed reference point.

Key Concept: Reference Point

c) Reference point
[Solution Description]
From the syllabus, a reference point is defined as a fixed object or point used to describe the position of another object. The correct answer is 'reference point'.

Key Concept: Reference Point, Position Change

d) Assertion is false, but Reason is true.
[Solution Description]
The assertion claims that a stationary reference point is necessary for accurately describing an object's position. However, a reference point can be moving or stationary—what matters is its fixed state during measurement. For instance, kilometre stones use Delhi as a reference point, even though Delhi itself moves due to Earth’s rotation. The reason states that a moving reference point creates ambiguity, which is true because relative motion between the object and reference point complicates position description. The reason correctly explains why the assertion is false. Thus:
- Assertion (A) is false: A reference point need not be stationary (e.g., Delhi as a moving reference point).
- Reason (R) is true: Motion in the reference point introduces ambiguity.

Key Concept: Reference Point and Motion

c) The car is 60 km away from the reference point.
[Solution Description]
The car starts from the reference point (starting point). After 1 hour, the car moves away at a speed of 60 km/h. Therefore, its distance from the reference point is: $distance = speed \times time = 60 \, \text{km/h} \times 1 \, \text{h} = 60 \, \text{km}$. So, the car is 60 km away from the reference point.

Key Concept: Kilometre Stone Example

b) The current location is 70 km away from Delhi
[Solution Description]
Kilometre stones indicate the distance from a reference point (e.g., Delhi). Here, the position is 70 km away from Delhi, which serves as the reference point.

Key Concept: Motion, Rest, Reference Point

b) Delhi 10 km
[Solution Description]
The car moves from 'Delhi 50 km' to 'Delhi 30 km' in 20 minutes. This means it covers 20 km in 20 minutes, confirming its speed as 60 km/h. Continuing at this speed for another 20 minutes will cover an additional 20 km, making the position 'Delhi 10 km'.

Key Concept: Reference Point and Motion

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a passenger inside a moving bus is at rest with respect to the bus. This is true because if the bus is chosen as the reference point, the passenger's position does not change relative to the bus.
The Reason explains that since the bus is the reference point, the passenger's position remains unchanged relative to it. This correctly justifies the Assertion because the definition of rest depends on the reference point chosen.
Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Relative Motion, Reference Point

c) It is impossible to determine without external observations.
[Solution Description]
According to the syllabus, if the ship is moving at a constant speed on a calm sea with no windows, there is no way to detect its motion internally because:
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Key Concept: Observation from Different Perspectives

c) Because they use different reference points.
[Solution Description]
Observations differ because people use different reference points to measure distance. For example, if each person uses their own house as a reference point, their observations will vary, even for the same object.

Key Concept: Reference Point

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that the distance from Deepa’s house to the garden differs based on whose house is being considered as the starting point. This is true, as distances can vary depending on the reference point used. The Reason defines what a reference point is, which is also correct and accurately explains why the distances appear different when measured from different houses. Therefore, both statements are correct, and the Reason provides the correct explanation for the Assertion.

Key Concept: Reference point, relative position

b) 9 km
[Solution Description]
First, find the distance each person has to travel to reach the garden:
1. Distance from Deepa's house to the garden:
- Deepa's house is 3 km east of bus stand.
- Garden is 4 km west of bus stand.
- Total distance = 3 km (east to bus stand) + 4 km (west to garden) = 7 km.
2. Distance from Anish's house to the garden:
- Anish's house is 5 km east of bus stand.
- Garden is 4 km west of bus stand.
- Total distance = 5 km + 4 km = 9 km.
3. Distance from Hardeep's house to the garden:
- Since Hardeep thinks both distances are equal, assume his house is equidistant from school and garden.
- From Fig. 5.9, this implies his house is near the bus stand, but exact distance isn't specified. However, since the garden is 4 km from the bus stand, his distance is exactly 4 km.
Thus, Anish has the longest journey (9 km).

Key Concept: Reference Point, Position Description

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that distances from different houses (Deepa's and Anish's) to the garden vary because their reference points are different. This is true because the concept of a reference point is fundamental in describing positions. The reason explains that a reference point is a fixed location used to measure distances, which is also true. Moreover, the reason correctly explains why the assertion is true: varying reference points lead to different measured distances. Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion.

Key Concept: Motion and Rest, Reference Point

c) It is impossible to determine without an external reference
[Solution Description]
Since there are no external reference points (e.g., no windows to observe objects outside), and the ship is moving at a constant speed without acceleration, the person cannot detect any motion. This is because motion is relative, and without a reference point, the state of rest or uniform motion remains indistinguishable (Galilean relativity).

Key Concept: Relative Motion

c) The bus is moving forward and the trees are stationary.
[Solution Description]
The person inside the bus is using the bus as a reference point. Since the trees appear to move backward, it means the bus is moving forward relative to the trees. Therefore, the motion of the trees is due to the motion of the bus.

Key Concept: Motion and Reference Point

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, an object is said to be at rest if its position does not change with respect to the reference point over time. If the reference point is inside the train (like another passenger or a seat), the passenger's position relative to that reference point remains constant as both are moving together. Therefore, the passenger is at rest relative to the train. The reason correctly explains why the assertion is true because it links the unchanging position of the passenger with respect to the reference point inside the train to the definition of rest.

Key Concept: Types of Motion

b) Circular motion
[Solution Description]
A merry-go-round moves along a circular path. Therefore, the child experiences circular motion as they rotate around the fixed central axis of the ride.

Key Concept: Oscillatory Motion, Linear Motion, Reference Point

c) Both oscillatory and linear motion
[Solution Description]
The pendulum exhibits oscillatory motion due to its back-and-forth swing. Its support's horizontal movement adds linear motion. For a stationary observer, the pendulum's path combines these two motions: oscillatory (vertical) + linear (horizontal), resulting in a wavy (non-linear) trajectory. This is neither purely oscillatory nor purely linear but a combination of both.

Key Concept: Detecting Motion

c) It’s impossible without external reference
[Solution Description]
Without an external reference (like waves or land), uniform motion feels like rest due to inertia (absence of acceleration). Therefore, detecting motion internally is impossible without observing external objects or changes in speed.

Key Concept: Relative Motion

c) 10 km/h
[Solution Description]
Since both cars are moving in the same direction, the relative speed of Car B with respect to Car A is calculated by subtracting Car A's speed from Car B's speed. So, $60\, \text{km/h} - 50\, \text{km/h} = 10\, \text{km/h}$. Therefore, from Car A's perspective, Car B is moving at 10 km/h.

Key Concept: Motion and Reference Point

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a tree is at rest when observed from the ground as a reference point. This is correct because the position of the tree relative to the ground does not change over time. The reason explains that an object is at rest if its position remains unchanged with respect to the reference point over time, which directly supports and explains why the tree is at rest when observed from the ground. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Reference point, Motion definition

b) Car B is moving toward Car A at 20 km/h.
[Solution Description]
Step 1: Convert speeds to m/s for consistency (since distance is given in meters).
- Speed of Car A = $60 \times \frac{1000}{3600} = 16.\overline{6}$ m/s.
- Speed of Car B = $80 \times \frac{1000}{3600} = 22.\overline{2}$ m/s.
Step 2: Analyze relative motion.
- Both cars move in the same direction, so we subtract their speeds to get relative speed.
- Relative speed of Car B w.r.t. Car A = $22.\overline{2} - 16.\overline{6} = 5.\overline{5}$ m/s.
Step 3: Interpret the result.
- Since Car B is moving faster than Car A, the distance between them decreases over time.
- From Car A's perspective, Car B appears to be moving forward at 5.\overline{5} m/s.
- Conversely, from Car B's perspective, Car A appears to be moving backward at 5.\overline{5} m/s.

Key Concept: Relative Motion, Reference Point

b) The ball moves in a parabolic path
[Solution Description]
The passenger inside the train sees the ball falling vertically downward (at rest with respect to the train). However, an outside observer sees both the horizontal motion of the train and the vertical fall of the ball. Thus, the ball has both horizontal velocity (same as the train's speed) and vertical acceleration due to gravity. The path observed by the outside observer is a parabola.

Key Concept: Reference Point Importance

b) The car is at rest relative to the parking lot.
[Solution Description]
The car is parked and its position does not change with respect to the parking lot over time. Since the reference point is the parking lot, the car is at rest.

Key Concept: Motion Detection

c) She is moving towards Delhi.
[Solution Description]
The decreasing distance from Delhi indicates that Padma's position is changing with respect to Delhi (the reference point). Thus, she is moving towards Delhi.

Key Concept: Linear Motion

c) An eraser dropped from a height
[Solution Description]
Linear motion occurs when an object moves along a straight line. Among the given options, pushing a heavy box in a straight line is the correct example of linear motion.

Key Concept: Linear Motion

d) Linear motion
[Solution Description]
The box moves along a straight path when pushed. According to the syllabus, motion along a straight line is called linear motion. Examples include pushing a heavy box or an eraser falling straight down.

Key Concept: Periodic Motion

c) A swing moving to and fro
[Solution Description]
Periodic motion repeats itself after a fixed interval of time. Both circular motion (e.g., a merry-go-round) and oscillatory motion (e.g., a swing) are periodic. Among the given options, a swing moving to and fro is periodic.

Key Concept: Identifying Linear Motion

c) Linear motion
[Solution Description]
As per the syllabus, students marching in a straight-line path exhibit linear motion because they are moving along a straight line. This is explicitly mentioned in the syllabus as an example of linear motion.

Key Concept: Linear Motion and Reference Point

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Assertion (A) states that a freely falling object moves in a straight line towards the Earth, which is true as observed in examples like dropping an eraser or an orange from a tree. Reason (R) explains that this motion is linear because gravity acts vertically downward in a straight line, which is also correct and provides the correct explanation for the assertion. Therefore, both assertion and reason are true, and reason correctly explains the assertion.

Key Concept: Examples of Linear Motion

b) An eraser falling from a table
[Solution Description]
From the syllabus, examples of linear motion include a heavy box being pushed along a straight line, an eraser dropped from a height, and students marching in a straight-line path. A spinning top is not an example of linear motion.

Key Concept: Periodic Nature of Circular Motion

b) It is periodic because it repeats the same path again and again.
[Solution Description]
The syllabus states that if an object repeats its path after a fixed interval of time, its motion is periodic. Circular motion involves the object moving repeatedly along the same circular path, so it is periodic in nature.

Key Concept: Practical Example of Circular Motion

c) A child riding a merry-go-round at constant speed.
[Solution Description]
Uniform circular motion involves an object moving at a constant speed along a circular path. Among the given examples, the merry-go-round fits this description perfectly.

Key Concept: Circular Motion, Periodic Motion

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the motion of an eraser whirled in a circular path is periodic. This is true because periodic motion refers to any motion that repeats itself at regular intervals of time. For the eraser moving in a circular path, it completes one full revolution and returns to the same position repeatedly, making its motion periodic.
The reason given is that in circular motion, the object repeats its path after completing one full revolution around the center. This is also true and correctly explains why the assertion is true. The repetition of the path after each full revolution defines the periodicity of the motion.

Key Concept: Periodicity, Oscillatory Motion Characteristics

b) 2 seconds
[Solution Description]
The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity. The time period does not depend on the amplitude as long as the oscillations are small (simple harmonic motion). Since the question states that all other conditions remain the same, doubling the amplitude does not affect the time period.
First, calculate the original time period:
$T_{\text{original}} = \frac{\text{Total time}}{\text{Number of oscillations}} = \frac{40\, \text{s}}{20} = 2\, \text{s}.$
Since the time period remains unchanged when the amplitude is doubled, the new time period $T_{\text{new}}$ is still 2 s.

Key Concept: Oscillatory Motion

c) Oscillatory motion
[Solution Description]
The given description matches oscillatory motion, where an object moves repeatedly back and forth around a fixed point. Examples include swings and pendulums.

Key Concept: Periodic vs Non-periodic

c) Non-periodic linear motion
[Solution Description]
The syllabus defines periodic motion as repeating movement at fixed intervals. The car's speed variations depend on unpredictable traffic signals, making the motion non-repetitive in nature. Additionally, linear motion without repetition doesn't qualify as periodic, circular or oscillatory (refer Table 5.4 in syllabus).

Key Concept: Periodic Motion

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the motion of a swing is an example of oscillatory motion, which is correct as per the syllabus definition. The reason explains that oscillatory motion involves to-and-fro movement about a fixed position, which is also accurate and directly explains why the swing's motion is oscillatory. Hence, both the assertion and reason are true, and the reason correctly explains the assertion.