Chapter 4 · Let us assessTextbook page 85

Let Us Assess, Q1–Q7 – Solutions വിലയിരുത്താം

The first seven end-of-chapter questions: mass and weight from the centre of the Earth to its surface, a falling spring balance, a trip to the Moon, two objects meeting in mid-air (fully animated, on the Earth and on the Moon), weight on the Moon, heavy versus light falling objects, and the differences between mass and weight. Try each one yourself first.

📖 What you need (pages 4, 8, 10 and 11 of this guide)

Question 1 · From the centre of the Earth to the surface

1. ഭൂകേന്ദ്രത്തിൽ നിന്ന് ഒരു വസ്തു ഭൗമോപരിതലം വരെ ഉയർത്തുകയാണെങ്കിൽ വസ്തുവിന്റെ മാസിനും ഭാരത്തിനും മാറ്റം ഉണ്ടാകുമോ? ഉത്തരം സാധൂകരിക്കുക. If an object is raised from the centre of the Earth to the Earth's surface, will its mass and its weight change? Justify your answer.

Does the amount of matter change on the way up? What is g at the centre, and what is it at the surface?

🧪 Raise a 10 kg object from the centre to the surface

Inside the Earth we use the textbook's simple picture: g grows steadily from 0 at the centre to 9.8 m/s² at the surface (as if the Earth had the same density everywhere).

Mass: no change. Mass is the quantity of matter in the object; nothing is added or removed by moving it.
Weight: changes – it increases. At the centre the Earth pulls equally from all sides, so g = 0 and the weight is zero. As the object is raised, g increases, and at the surface g = 9.8 m/s², so the weight becomes W = mg (for 10 kg, 98 N).
💡 Why this matters

It shows the difference between the two words in one line: the object carries its mass with it unchanged, but its weight depends on where it is.

Question 2 · A spring balance that falls

2. 5 kg മാസ് ഉള്ള ഒരു വസ്തുവിനെ സ്പ്രിങ് ബാലൻസിൽ തൂക്കിയിട്ട് ഭാരം നിർണ്ണയിച്ചു. വസ്തുവും സ്പ്രിങ് ബാലൻസും ഒരുമിച്ച് താഴേക്ക് പതിച്ചാൽ ആ അവസരത്തിൽ വസ്തുവിന്റെ ഭാരം എത്രയായിരിക്കും? കാരണമെന്ത്? An object of mass 5 kg was hung on a spring balance and its weight was found. If the object and the spring balance fall down together, what will be the weight of the object at that moment? What is the reason?

Both fall freely with the same acceleration g. Use reading = m(g − a) from page 11.

🎬 At rest, then falling together
Answer: At rest the balance reads 5 × 9.8 = 49 N. When the balance and the object fall together, the weight shown is zero. Reason: both are in free fall with the same acceleration g, so the object does not pull on the spring at all – the whole of the gravitational force is used to give it acceleration (reading = m(g − g) = 0). This is weightlessness. (Gravity still pulls it with 49 N – that is what makes it fall.)

Question 3 · Taken to the Moon

3. ഭൂമിയിൽ നിന്നും ചന്ദ്രനിൽ എത്തിക്കുന്ന വസ്തുവിന്റെ മാസ്, ഭാരം എന്നിവയിൽ മാറ്റം ഉണ്ടാകുമോ? ഉത്തരം സാധൂകരിക്കുക. Will there be any change in the mass and the weight of an object taken from the Earth to the Moon? Justify your answer.

Compare g on the Earth (9.8 m/s²) with g on the Moon (1.62 m/s²).

🖼️ A 60 kg student on the Earth and on the Moon
Mass: no change – the amount of matter is the same anywhere in the universe. Weight: decreases to about one-sixth. Weight W = mg, and g on the Moon (1.62 m/s²) is about 1/6 of g on the Earth (9.8 m/s²), because the Moon's mass is much smaller. Example: a 60 kg student weighs 60 × 9.8 = 588 N on the Earth but only 60 × 1.62 = 97.2 N on the Moon – still 60 kg of mass.

Question 4 · Two objects meet in mid-air

4. 100 m ഉയരമുള്ള ഒരു ടവറിന് മുകളിൽ നിന്ന് ഒരു വസ്തു നിർബാധം പതിക്കാൻ അനുവദിച്ചു. അതേസമയം മറ്റൊരു വസ്തു ഈ വസ്തുവുമായി കൂട്ടിമുട്ടത്തക്കരീതിയിൽ 25 m/s പ്രവേഗത്തോടെ നേരെ താഴെ നിന്നും കുത്തനെ മുകളിലേക്ക് എറിഞ്ഞു (gഭൂമി = 10 m/s², gചന്ദ്രൻ = 1.62 m/s²). An object is allowed to fall freely from the top of a tower 100 m high. At the same moment another object is thrown vertically upwards with a velocity of 25 m/s from directly below, so that the two will collide. (gEarth = 10 m/s², gMoon = 1.62 m/s²)

  1. After how much time will they meet? എത്ര സമയത്തിനുശേഷം അവ കൂട്ടിമുട്ടും?
  2. Calculate at what height above the ground they meet. തറയിൽ നിന്ന് എത്ര ഉയരത്തിൽ വച്ചായിരിക്കും കൂട്ടിമുട്ടുന്നത്?
  3. If this is done on the Moon, will the answers change? Justify. ഈ പ്രവർത്തനം ചന്ദ്രനിൽ വച്ചാണ് നടത്തിയതെങ്കിൽ ലഭിച്ച ഉത്തരങ്ങൾക്ക് മാറ്റം ഉണ്ടാകുമോ?

Call the meeting time t. The top object has fallen ½gt²; the bottom one has risen 25t − ½gt². At the meeting point these two distances add up to the height of the tower, 100 m. Watch what happens to the ½gt² terms!

🎬 Solution animation – exam layout
🎞️ Watch them meet – positions against time

Switch between the Earth and the Moon: the meeting time stays at 4 s, but the meeting height changes from 20 m to 87.04 m. On the Moon both objects move much more gently, so the thrown one gets much higher before the falling one reaches it.

🧪 Try other numbers
Answer: Let them meet after t s. Fallen by the top object s₁ = ½gt²; risen by the bottom object s₂ = 25t − ½gt². Meeting: s₁ + s₂ = 100 ⇒ 25t = 100.
(a) t = 4 s.
(b) s₁ = ½ × 10 × 4² = 80 m, so they meet 20 m above the ground (check: s₂ = 25 × 4 − 80 = 20 m ✓).
(c) On the Moon the time does not change – still 4 s, because g cancelled out (t = height ÷ throw speed = 100 ÷ 25). The height changes: s₁ = ½ × 1.62 × 4² = 12.96 m, so they meet 87.04 m above the ground.
⚠️ Common trap

Trying to solve two separate equations with g in each and getting lost. Add the two distances first – the ½gt² terms cancel. Relative to each other, the two objects simply close the 100 m gap at 25 m/s, because gravity pulls both equally.

💡 Why this matters

“Gravity accelerates everything equally” is a powerful shortcut. Seen from the falling object, the thrown one just comes straight at it at a steady 25 m/s – on the Earth, on the Moon, anywhere.

Question 5 · One-sixth gravity

5. ചന്ദ്രോപരിതലത്തിൽ ഗുരുത്വാകർഷണബലം ഭൂമിയിലേതിന്റെ ഏകദേശം 1/6 ആണ്. a) 10 kg മാസുള്ള വസ്തുവിന്റെ ഭൂമിയിലെ ഭാരം എത്രയായിരിക്കും? b) ഈ വസ്തു ചന്ദ്രോപരിതലത്തിൽ എത്തിച്ചാൽ അതിന്റെ മാസ് എത്ര? ഭാരം എത്ര? On the surface of the Moon the gravitational force is about 1/6 of that on the Earth.

  1. What will be the weight on the Earth of an object of mass 10 kg?
  2. If this object is taken to the surface of the Moon, what is its mass? What is its weight?

W = mg with g = 9.8 m/s². On the Moon the mass is unchanged and the weight is one-sixth.

🎬 Solution animation – exam layout
🧪 Try other numbers
Answer: (a) Weight on the Earth W = mg = 10 × 9.8 = 98 N.
(b) On the Moon the mass is still 10 kg. Weight = 1/6 × 98 ≈ 16.3 N. (Using gMoon = 1.62 m/s²: 10 × 1.62 = 16.2 N – the same answer to within rounding.)

Question 6 · Heavy and light – which lands first?

6. മാസ് കൂടിയ വസ്തുക്കളെയാണ് മാസ് കുറഞ്ഞ വസ്തുക്കളെക്കാൾ കൂടുതൽ ശക്തമായി ഭൂമി ആകർഷിക്കുക. എങ്കിൽ മാസ് കൂടിയ വസ്തുവും മാസ് കുറഞ്ഞ വസ്തുവും ഒരേ ഉയരത്തിൽ നിന്നും നിർബാധം പതിക്കാൻ അനുവദിച്ചാൽ, a) ഏതാണ് ആദ്യം തറയിൽ എത്തുക? b) ഉത്തരം സാധൂകരിക്കുക. The Earth attracts objects of greater mass more strongly than objects of smaller mass. Then, if a heavier object and a lighter object are allowed to fall freely from the same height, (a) which one reaches the ground first? (b) Justify your answer.

Bigger force – but also more mass to move. What is a = F/m for each?

🎬 Bigger pull, bigger mass – same acceleration
(a) Both reach the ground at the same time (in free fall, i.e. ignoring air).
(b) The Earth does pull the heavier object harder: F = GMm/R² is proportional to m. But the heavier object also has more mass (more inertia) to accelerate. Acceleration a = F/m = (GMm/R²)/m = GM/R² = g – the mass m cancels. Both fall with the same acceleration g = 9.8 m/s² from the same height, so they take the same time.

Question 7 · How do mass and weight differ?

7. മാസും ഭാരവും എങ്ങനെയെല്ലാം വ്യത്യാസപ്പെട്ടിരിക്കുന്നു എന്ന് വിശദമാക്കുക. Explain in what ways mass and weight differ from each other.

Five headings: what it is, how it is measured, its unit, whether it changes from place to place, and whether it can be zero.

🗂️ Sort the statements – mass or weight?
Score: 0 / 0
Mass മാസ്Weight ഭാരം
The quantity of matter in an object.The force with which the Earth (or another celestial body) attracts the object.
Measured with a common balance.Measured with a spring balance or a platform balance.
SI unit: kilogram (kg).SI unit: newton (N); also kgwt (1 kgwt = 9.8 N).
The same everywhere in the universe.Changes with g: more at the poles, less at the equator, about 1/6 on the Moon.
Never zero.Zero at the centre of the Earth (and shows zero in free fall).
Has only a size (a scalar).Is a force: has a size and a direction – towards the centre of the Earth.

Check yourself

Next: Let us assess, Q8–Q14 and extended activities ▶