Everything in the universe pulls everything else! This pull is called gravitational force. It makes apples fall, keeps moon around Earth, and planets around the Sun.
Centripetal force: For circular motion, a force towards the centre is needed. For moon, that centre‑seeking force is gravity.
Importance: explains why we stay on Earth, moon's motion, tides, planets around Sun.
📘 In-text questions
Q1. State the universal law of gravitation.
Ans: Every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts along the line joining their centres.
Q2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Ans: F = G · (M × m) / R², where M = mass of earth, m = mass of object, R = radius of earth.
Free fall means falling only under gravity – no air resistance, no parachute. In free fall, all objects speed up at the same rate, no matter their mass.
This rate is called acceleration due to gravity, symbol g. On Earth, g = 9.8 m/s² (we often use 10 for easy maths).
From universal law: Force on object of mass m near Earth: F = G·M·m / R². But also F = m·g.
So m·g = G·M·m / R² ⇒ g = G·M / R².
If object is thrown upward, we take a = –g.
📘 In-text questions
Q1. What do you mean by free fall?
Ans: When an object falls towards the earth only under gravitational force (no other force like air resistance), it is called free fall.
Q2. What do you mean by acceleration due to gravity?
Ans: The acceleration experienced by an object during free fall due to earth's gravitational pull. It is denoted by g and its value on earth is 9.8 m/s².
| Mass | Weight |
|---|---|
| Amount of matter in an object (kg) | Force with which earth attracts it (newton) |
| Same everywhere (constant) | Changes with place (depends on g) |
| Measured by pan balance | Measured by spring balance |
| Scalar (only magnitude) | Vector (downwards) |
Weight = mass × g (W = m g)
Mass of moon Mm = 7.36×10²² kg, radius Rm = 1.74×10⁶ m.
g on moon = G·Mm/Rm² = about 1.6 m/s² (≈ 1/6 of Earth's g).
So weight on moon = (1/6) × weight on Earth.
📘 In-text questions
Q1. What are the differences between mass and weight?
Ans: See table above.
Q2. Why is weight on moon 1/6 that on earth?
Ans: Because moon's mass is smaller and radius is smaller, so g on moon = G·Mm/Rm² ≈ 1.6 m/s², while Earth's g = 9.8 m/s². Ratio ≈ 1/6.
Thrust: force acting perpendicular to a surface (like when you push a drawing pin).
Pressure: thrust per unit area. Pressure = Thrust / Area
SI unit of pressure: pascal (Pa) = N/m². Smaller area → larger pressure for same force.
📘 In-text questions
Q1. Why is it difficult to hold a school bag with a thin strap?
Ans: Thin strap has small area, so pressure (force/area) on shoulder is large, causing pain.
Q2. What do you mean by buoyancy?
Ans: The upward force exerted by fluids (liquids or gases) on objects immersed in them.
Q3. Why does an object float or sink?
Ans: If density of object is less than density of liquid → float; if more → sink. (Because buoyant force depends on displaced liquid's weight).
Buoyant force (upthrust) is the upward push by fluid. It happens because pressure increases with depth, so bottom of object experiences more upward force than downward force on top.
Density = mass/volume. If object density < fluid density → buoyant force > weight → object floats. If density > fluid density → sinks.
Applications: designing ships, submarines, hydrometers, lactometers.
📘 In-text questions
Q1. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Ans: The weighing machine measures weight, but shows mass assuming g=9.8. Actually, due to buoyancy of air, your true mass is slightly more than 42 kg (because air pushes you up a little). But the difference is tiny.
Q2. A bag of cotton and an iron bar, each 100 kg on weighing machine. Which is heavier in reality?
Ans: Cotton has larger volume, so more air buoyant force acts on it. The weighing machine measures weight – buoyancy. So cotton's true mass is slightly more than iron's to show same reading. So cotton is heavier in reality.
| Q.No. | Answer / Solution (step by step) |
|---|---|
| 1. | How does force change when distance is halved? F ∝ 1/d², so if d becomes half, F becomes 1/(½)² = 4 times. Force becomes 4 times. |
| 2. | Why do heavy and light objects fall at same rate? Because acceleration due to gravity (g) is independent of mass. F = ma and F = GMm/R² ⇒ a = GM/R² = g (same for all). |
| 3. | Gravitational force between Earth and 1 kg object on surface. F = G·M·m/R². Using M=6×10²⁴ kg, R=6.4×10⁶ m, G=6.67×10⁻¹¹, m=1 kg. Calculate: F = (6.67×10⁻¹¹ × 6×10²⁴ × 1) / (6.4×10⁶)² ≈ 9.8 N. |
| 4. | Does Earth attract moon with greater force than moon attracts Earth? No, same force (Newton's third law). But accelerations differ due to different masses. |
| 5. | If moon attracts Earth, why doesn't Earth move towards moon? Earth does move, but very little because its mass is huge. Both move around common centre of mass (inside Earth). |
| 6. | Force between two objects changes if: (i) mass of one doubled → force doubles. (ii) distance doubled → force becomes 1/4; distance tripled → force becomes 1/9. (iii) masses of both doubled → force becomes 4 times. |
| 7. | Importance of universal law of gravitation: It explains (i) why we stay on Earth, (ii) motion of moon around Earth, (iii) planets around Sun, (iv) tides. |
| 8. | Acceleration of free fall: It is the acceleration due to gravity, g = 9.8 m/s². |
| 9. | What do we call gravitational force between Earth and an object? Weight of the object. |
| 10. | Amit buys gold at poles, sells at equator. Will friend agree with weight? No, because g is greater at poles than equator, so weight at poles > weight at equator. But mass remains same. So at equator weight is less – friend gets less gold (in terms of force), but mass wise it's same. (Hint: g changes). |
| 11. | Why does a sheet of paper fall slower than crumpled ball? Because flat paper experiences more air resistance (upthrust from air), so net downward force less. Crumpled ball has less air resistance. |
| 12. | Weight on moon of 10 kg object? On Earth weight = 10×9.8 = 98 N. On moon weight = 98/6 ≈ 16.3 N. (Or using g_moon = 1.63 m/s² ⇒ 10×1.63 = 16.3 N). |
| 13. | Ball thrown up with 49 m/s. (i) max height? (ii) total time to return? (i) v² = u² – 2gh ⇒ 0 = 49² – 2×9.8×h ⇒ h = (2401)/(19.6) = 122.5 m. (ii) time up = u/g = 49/9.8 = 5 s, total time = 10 s. |
| 14. | Stone dropped from 19.6 m. Final velocity? v² = u² + 2gh = 0 + 2×9.8×19.6 = 384.16 ⇒ v = √384.16 = 19.6 m/s. |
| 15. | Stone thrown up with 40 m/s, g = 10. Max height? Net displacement? Total distance? max height: v² = u² – 2gh ⇒ 0 = 1600 – 20h ⇒ h = 80 m. Net displacement after return = 0. Total distance = 80+80 = 160 m. |
| 16. | Force between Earth and Sun: M_earth=6×10²⁴ kg, M_sun=2×10³⁰ kg, d=1.5×10¹¹ m, G=6.7×10⁻¹¹. F = (6.7×10⁻¹¹ × 6×10²⁴ × 2×10³⁰)/(1.5×10¹¹)² = (6.7×12×10⁴³)/(2.25×10²²) = (80.4×10⁴³)/(2.25×10²²) = 35.73×10²¹ = 3.57×10²² N. |
| 17. | Stone A dropped from tower 100 m, stone B thrown up at 25 m/s from ground. When and where meet? Let upward positive. For A (from top): position s_A = 100 – ½gt². For B (from ground): s_B = 25t – ½gt². They meet when s_A = s_B ⇒ 100 – ½gt² = 25t – ½gt² ⇒ 100 = 25t ⇒ t = 4 s. Then s_B = 25×4 – ½×10×16 = 100 – 80 = 20 m above ground. So meet at 20 m from ground after 4 s. |
| 18. | Ball thrown up returns after 6 s. (a) velocity thrown? (b) max height? (c) position after 4 s? Total time = 6 s ⇒ time up = 3 s. (a) v = u – gt ⇒ 0 = u – 9.8×3 ⇒ u = 29.4 m/s. (b) max height = u t – ½gt² = 29.4×3 – ½×9.8×9 = 88.2 – 44.1 = 44.1 m. (c) after 4 s (1 s after top): position = max height – ½g(1)² = 44.1 – 4.9 = 39.2 m above ground. |
| 19. | Direction of buoyant force on immersed object? Upward (opposite to weight). |
| 20. | Why does plastic block come up in water? Density of plastic < density of water ⇒ buoyant force > weight ⇒ net upward force. |
| 21. | Volume of 50 g substance = 20 cm³. Density = 50/20 = 2.5 g/cm³ > density of water (1 g/cm³). So it will sink. |
| 22. | 500 g sealed packet volume 350 cm³. Density = 500/350 ≈ 1.43 g/cm³ > 1 g/cm³ ⇒ sink. Water displaced = volume of packet = 350 cm³ ⇒ mass of displaced water = 350 g. |