Filling and Lifting — NCERT Solutions

Answer: A bucket holds ☑ more than 1 litre of water.

Reason: A standard bucket holds about 10–15 litres of water, which is much more than 1 litre.

Answer: A mug holds ☑ less than half a litre of water.

Reason: A standard mug holds about 200–300 ml, which is less than half a litre (500 ml).
(Students should verify this by pouring water from a half-litre measure into their mug.)

Answer: A glass holds ☑ more than a quarter litre of water.

Reason: A standard drinking glass holds about 200–250 ml, and a quarter litre = 250 ml. Most glasses hold approximately equal to or slightly less than a quarter litre.

(Note: Answers may vary. Students should verify by pouring a quarter litre of water into their glass at home.)

Answer: Chintu is holding 3 textbooks in one hand and a pencil box in the other hand.

The hand holding the 3 textbooks is lower because the textbooks are heavier than the pencil box.

Concept: Heavier objects pull the hand downward due to their greater weight. This is the same principle used in a pan-balance — the heavier side goes down.

Concept: When you hold two objects, the heavier one makes your hand go lower. Compare by feel.

Sample Observations:

(Actual observations may vary slightly based on the specific items, but the general answers above are expected.)

Concept: A simple pan-balance is used. Place the object on one side and add coins or erasers on the other side until both sides are balanced. The number of coins/erasers needed equals the weight of the object in those units.

Method:

1. Place the object (e.g., pencil) on one pan of the balance.
2. Add coins/erasers one by one to the other pan.
3. Count the coins/erasers when the balance is level.

Sample Table (answers will vary):

(Students should fill in actual values from their activity.)

Concept: A matchbox filled with sand acts as a standard unit of weight. Place the object on one pan and add matchboxes on the other pan until balanced.

Method:

1. Fill a matchbox with sand — this is your unit weight.
2. Place the object on one pan.
3. Add matchboxes one by one to the other pan until balanced.
4. Count the matchboxes.

Sample Table (answers will vary):

Order from lightest to heaviest (sample):
Spoon → 4 Marbles → Pencil box

(Students should record their own measured values and arrange accordingly.)

Answer: A bag is heavier or lighter depending on:

• The number of books and notebooks it contains.
• The size and weight of each book.
• Other items like water bottles, lunch boxes, pencil boxes, etc.

A bag with more books or heavier items will be heavier than a bag with fewer or lighter items.

Activity-based answer. Students should count the books in their bag and in their friend's bag.

Expected finding: The bag with more books (or heavier books) will generally be heavier. If one bag has 6 books and another has 4 books, the bag with 6 books is likely heavier.

Answer: Yes, we can make the two bags approximately the same weight by moving a book from the heavier bag to the lighter bag.

Method:

1. Identify the heavier bag and the lighter bag.
2. Move one book from the heavier bag to the lighter bag.
3. Check again using the pan-balance or by feel.
4. Repeat if needed until both bags feel approximately equal in weight.

Conclusion: By transferring books, we can balance the weight of the two bags.

Activity-based question. Students should look for objects at home with '1 kg' written on them.

Sample Answer: Objects that are commonly 1 kilogram:

• 1 kg salt packet
• 1 kg sugar packet
• 1 kg rice packet
• 1 kg flour (atta) packet
• 1 kg dal packet

(Answers will vary based on what is available at home.)

Concept: Use the feel of a 1 kg salt packet as a reference. Compare other objects to it.

General guidelines:

• Objects that feel lighter than the 1 kg packet → less than 1 kg
• Objects that feel heavier than the 1 kg packet → more than 1 kg

Sample answers (based on common objects shown in such activities):

• A pencil → less than 1 kg
• A school bag (full) → more than 1 kg
• An apple → less than 1 kg
• A brick → more than 1 kg
• A notebook → less than 1 kg

(Students should tick based on their own comparison with the 1 kg packet.)

Given: From the picture, two daal packets together balance a 1 kg weight on the pan-balance.

Concept: If 2 packets = 1 kg, then each packet = $\frac{1}{2}$ kg.

$$2 \times \text{weight of each packet} = 1 \text{ kg}$$
$$\text{Weight of each packet} = \frac{1}{2} \text{ kg}$$

Answer: Each daal packet weighs ☑ half kilogram.

Given: From the picture, four tea packets together balance a 1 kg weight on the pan-balance.

Concept: If 4 packets = 1 kg, then each packet = $\frac{1}{4}$ kg.

$$4 \times \text{weight of each packet} = 1 \text{ kg}$$
$$\text{Weight of each packet} = \frac{1}{4} \text{ kg}$$

Answer: Each tea packet weighs ☑ quarter kilogram.

Given: 3 balls — one is heavier, two are equal in weight. Only a pan-balance is available (no weights).

Answer: You will have to weigh only 1 time.

Explanation: Place one ball on each pan of the balance (any two balls).

• If one side goes down → that ball is the heavy ball. Done in 1 weighing.
• If both sides are equal → the third ball (not on the balance) is the heavy ball. Done in 1 weighing.

In both cases, the heavy ball is identified in just one weighing.

Method (using the balance only once):

Step 1: Label the three balls as Ball A, Ball B, and Ball C.

Step 2: Place Ball A on the left pan and Ball B on the right pan.

Step 3: Observe the balance:

• If left side (Ball A) goes down → Ball A is the heavy ball.
• If right side (Ball B) goes down → Ball B is the heavy ball.
• If both sides are equal → Ball C (the one not placed on the balance) is the heavy ball.

Conclusion: In just one weighing, we can identify the heavy ball.

Given: Three balls — Red, Orange, Green — all different weights. Pan-balance available, no standard weights.

Strategy: We need at least 2 weighings to find the order of all three.

Step 1 — First Weighing:
Place the Red ball on the left pan and the Orange ball on the right pan.

• Suppose Red goes down → Red is heavier than Orange.

Step 2 — Second Weighing:
Place the Red ball on the left pan and the Green ball on the right pan.

• Case A: If Red goes down → Red is heavier than Green too.
• Now compare Orange and Green: place Orange vs Green.
• Whichever goes down is heavier.
• This gives the full order.
• Case B: If Green goes down → Green is heavier than Red.
• We already know Red > Orange, and Green > Red.
• So order is: Green (heaviest) > Red > Orange (lightest).

General Method:

1. Weigh any two balls (e.g., Red vs Orange).
2. Weigh the heavier one against the third ball (Green).
3. From the results, determine the complete order: heaviest → middle → lightest.

Conclusion: Using 2 to 3 weighings, we can find which ball is the heaviest and which is the lightest by comparing them on the pan-balance two at a time.