Chapter 4 · ApplicationsGravity in real lifeExplore online

Applications & Explore Online ഗുരുത്വാകർഷണം

Gravity is not only a chapter in the textbook: it decides how much you weigh on Jupiter, how fast a coconut hits the ground, why astronauts float, why the sea at Kochi rises twice a day and how ISRO sent Chandrayaan-3 to the Moon. Every lab below uses only the formulas of this chapter.

📖 The ideas behind every lab

1. Your weight on other worlds

Your mass (മാസ്) – the amount of matter in you – is the same everywhere. Your weight (ഭാരം) is the pull of the planet or moon you stand on, W = mg, so it changes with g. The g values are the ones in Table 4.4 of your textbook (plus the Moon and Jupiter from “Let us assess”, Q14).

⚖️ Planet-weight calculator: W = m × g

Bar length is proportional to g, so it is also proportional to the weight. A spring balance stretches more where the pull is bigger; a common balance (കോമൺ ബാലൻസ്) would balance the same standard masses on every world.

📝 In the exam this looks like: “Find the weight of a 100 kg object at the centre of the Earth, at the poles, at the equator, on the Moon and on Jupiter (g = 23.1 m/s2).” → 0 N, 983 N, 978 N, 162 N, 2310 N (W = mg each time; mass stays 100 kg).

2. The falling coconut

Kerala’s tall coconut palms are often 15–25 m high. A coconut that breaks off is in free fall (നിർബാധ പതനം): it starts from rest (u = 0) and gains 9.8 m/s of speed every second. From s = ut + ½at2 with u = 0 and a = g, the time to fall a height h is t = √(2h/g), and it hits the ground with v = gt. Its mass does not appear anywhere – a big coconut and a small one fall together.

🥥 Coconut-fall timer: t = √(2h/g), v = gt

The faint coconuts show where it was every 0.25 s. The gaps grow because the speed keeps increasing – that is what an acceleration looks like.

⚠ Never stand, play or park a scooter under a coconut palm, especially in monsoon wind. A coconut of 1–2 kg falling from 15 m arrives at about 60 km/h. Climbers use a safety belt; harvest only with an adult’s help.

📝 In the exam this looks like: “A stone dropped from the top of a building reaches the ground in 2 s (g = 9.8 m/s2). Find the height and the speed just before it touches the ground.” → h = ½gt2 = ½ × 9.8 × 22 = 19.6 m; v = gt = 9.8 × 2 = 19.6 m/s (Let us assess, Q9).

3. Newton’s cannon – how a satellite stays up

Newton imagined a cannon on a mountain so high that there is no air. Fire a ball sideways and it falls to the ground in a curve. Fire it faster and it lands farther away. Fire it at about 7.9 km/s and the ground curves away beneath it as fast as it falls: it keeps falling around the Earth for ever – it is in orbit. The Earth’s gravity is the centripetal force (അഭികേന്ദ്രബലം) that bends its path; this is exactly how an artificial satellite (കൃത്രിമ ഉപഗ്രഹം) works.

🚀 Newton’s cannon / orbit simulator
below ≈ 7.9 km/sfalls back to the ground
≈ 7.9 km/scircles the Earth (orbit) in about 85–90 min
7.9 – 11.2 km/san oval (elliptical) orbit
11.2 km/s or moreescapes from the Earth

The path is worked out step by step from F = GMm/r2 with the textbook values G = 6.67 × 10−11 N m2/kg2, M = 6 × 1024 kg, R = 6.4 × 106 m, firing from 64 km up (1 % of R). Heights above the ground are stretched in the picture so that you can see the paths; the directions and distances along the ground are true. Air is ignored – a real ball fired this fast in air would burn up.

📝 In the exam this looks like: “Where do artificial satellites get the centripetal force needed to go round the Earth?” → From the Earth’s gravitational force; gravity itself acts as the centripetal force, directed towards the centre of the Earth.

4. The International Space Station – gravity is still there!

Astronauts float inside the ISS, so many people think there is no gravity in space. Use g = GM/r2: at a distance r from the centre, g = 9.8 × (R/r)2. At 400 km up, r = 6400 + 400 = 6800 km and g ≈ 8.7 m/s2 – about 89 % of the value on the ground. The astronauts float because the station and everything in it are in free fall together, all accelerating at the same g: nothing presses on the floor, so a weighing scale reads zero (ഭാരമില്ലായ്മ, weightlessness).

🛰️ Gravity at a height: g = 9.8 × (R / (R + h))²

The orbit speed shown is the speed for which gravity is exactly the centripetal force needed for a circle of radius R + h. India’s Gaganyaan astronauts are planned to orbit at about 400 km too.

📝 In the exam this looks like: “Why do astronauts in a space station orbiting the Earth feel weightless?” → The station and the astronauts fall freely together with the same acceleration; the whole of the gravitational force is used to produce that acceleration, so nothing supports them and a balance reads zero. Gravity there is not zero (≈ 89 % of its value on the ground).

5. Tides at Kochi

Twice a day the sea at Fort Kochi and Vizhinjam rises (high tide, വേലിയേറ്റം) and falls (low tide, വേലിയിറക്കം). The Moon pulls every part of the Earth, but by the inverse-square law it pulls the near side about 3 % more strongly than the Earth’s centre and the far side about 3 % less. So the ocean bulges towards the Moon on the near side and is “left behind” on the far side – two bulges. As the Earth turns, Kochi passes through both bulges: two high tides about 12 h 25 min apart. The Sun does the same, more weakly; at new moon and full moon the two pulls line up and the tides are biggest (spring tides).

🌊 Two bulges, two high tides

View from above the North Pole; the Earth spins once a day while the Moon moves only about 13° along its orbit, so the same tide comes back after about 24 h 50 min. The bulges and the arrows are hugely exaggerated – Kochi’s tides are gentle, usually less than about 1 m from low to high.

📝 In the exam this looks like: “The Sun and the Moon exert a force on the Earth. Give one evidence.” → Tides: the regular rise and fall of the sea level (വേലിയേറ്റം, വേലിയിറക്കം) is caused by the gravitational pull of the Moon (and the Sun) on the Earth’s water – so all bodies in the universe attract one another.

6. Rockets, Sriharikota and Chandrayaan-3

To leave the Earth a spacecraft must work against the Earth’s gravity, and that needs a huge amount of energy – a huge rocket full of fuel. ISRO’s LVM3 weighs about 640 tonnes at lift-off, almost all of it fuel. Instead of firing straight at the Moon (which would need an even bigger rocket), Chandrayaan-3 was put into a long orbit around the Earth and its own engine raised that orbit step by step, each time at the point closest to the Earth. Finally the Moon’s gravity captured it. This clever technique let India use a smaller, much cheaper rocket.

🌙 Chandrayaan-3, step by step (not to scale)
🔭 Go further (not in the exam): escape speed

Throw a stone up faster and faster: at about 11.2 km/s it would never come back from the Earth (ignoring air). From the Moon, where g is only 1.62 m/s2, about 2.4 km/s is enough. That is why leaving the Earth needs giant rockets, while the Chandrayaan lander could fire small engines on the Moon. Landing is the reverse problem: if Vikram’s engines had stopped 100 m above the surface, it would have hit the Moon at v = √(2gh) = √(2 × 1.62 × 100) = 18 m/s, about 65 km/h – a crash. Its engines kept slowing it down so it could touch down gently.

📝 In the exam this looks like: “Chandrayaan-3 landed softly on the Moon. While coming down, the speed of the lander increases. Why? How was a soft landing made possible?” → The Moon’s gravitational force accelerates the lander towards the Moon; its engines were fired against the motion to reduce the speed gradually until it touched down gently (soft landing, സോഫ്റ്റ് ലാൻഡിങ്).

✅ Check yourself

🌐 Explore online – resources hub

Everything in this guide works offline. The links below are extras: simulations, short videos and articles from trusted sources (PhET, NASA, ISRO and others), grouped by topic. They need internet and open in a new tab, so you will not lose your place here. Ask a parent or teacher before you go online. The PhET simulations run directly in your browser – nothing to install.

Universal law of gravitation

🌐 Universal law of gravitation needs internet · opens in a new tab

Measuring G (Cavendish)

🌐 Measuring G (Cavendish) needs internet · opens in a new tab

Free fall and g

🌐 Free fall and g needs internet · opens in a new tab

Feather and coin

🌐 Feather and coin needs internet · opens in a new tab

Why g changes from place to place

🌐 Why g changes from place to place needs internet · opens in a new tab

Mass and weight

🌐 Mass and weight needs internet · opens in a new tab

Weightlessness and microgravity

🌐 Weightlessness and microgravity needs internet · opens in a new tab

Circular motion

🌐 Circular motion needs internet · opens in a new tab

Satellites, Chandrayaan and ISRO

🌐 Satellites, Chandrayaan and ISRO needs internet · opens in a new tab

Thanu Padmanabhan

🌐 Thanu Padmanabhan needs internet · opens in a new tab

Black holes

🌐 Black holes needs internet · opens in a new tab

Tides

🌐 Tides needs internet · opens in a new tab

Malayalam explainers

🌐 Malayalam explainers needs internet · opens in a new tab

More to explore

🌐 More to explore needs internet · opens in a new tab
🧭 Next

Now pull the whole chapter together: Summary & Quick Quiz ▶