Physics · 1st Puc Science

Ch 7Gravitation — 1st PUC Physics, concept-first.

Long before we ever study physics, we know the pull of the Earth. A ball thrown up always comes down. Walking uphill is harder than walking downhill. Rain falls from clouds, not up into the sky. These everyday experiences point to a fundamental truth: all material objects are attracted towards the Earth.

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Conservation of Angular Momentum

Imagine you're sitting on a spinning office chair with your arms stretched out. Someone gives you a gentle push, and you start rotating slowly. Now pull your arms in tight against your chest.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

7.1

Introduction

Long before we ever study physics, we know the pull of the Earth. A ball thrown up always comes down. Walking uphill is harder than walking downhill. Rain falls from clouds, not up into the sky.

7.2

Kepler's Laws

The motion of planets across the night sky had been studied for centuries before Johannes Kepler, working with the precise observations of Tycho Brahe, finally broke free from the ancient assumption t…

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Example 7.1Let the speed of the planet at the perihelion $P$ in Fig. 7.1(a) be $v_P$ and the Sun-planet distance $SP$ be $r_P$. Relate $\{r_P, v_P\}$ t…Preview

7.3

Universal Law of Gravitation

Every object in the universe attracts every other object with a force. This is not a vague tendency — it is a precise, mathematical statement about the strength of that attraction.

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Example 7.2Three equal masses of $m$ kg each are fixed at the vertices of an equilateral triangle $ABC$. (a) What is the force acting on a mass $2m$ pl…Preview

7.4

The Gravitational Constant

The story of gravitation has two distinct halves. Newton gave us the law — the inverse-square relation that governs the force between any two masses.

7.5

Acceleration Due to Gravity of the Earth

When we drop a stone, it falls toward the Earth. The force causing this motion is gravity. But what exactly is the acceleration that this force produces? That is the question this section answers.

7.6

Acceleration Due to Gravity Below and Above the Surface of Earth

The acceleration due to gravity is not a universal constant. Its value changes as we move away from the Earth's surface — either upward into the atmosphere or downward into the Earth's interior.

7.7

Gravitational Potential Energy

The concept of gravitational potential energy is central to understanding how objects interact in a gravitational field.

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Example 7.3Find the potential energy of a system of four particles placed at the vertices of a square of side $l$. Also obtain the potential at the cen…Preview

7.8

Escape Speed

When you throw a ball upward, it rises, stops, and falls back. The harder you throw it, the higher it goes.

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Example 7.4Two uniform solid spheres of equal radii $R$, but mass $M$ and $4M$ have a centre to centre separation $6R$, as shown in Fig. 7.10. The two…Preview

7.9

Earth Satellites

3 Q

An object that moves around a planet in a closed orbit is called a satellite. The Moon is Earth's natural satellite.

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Example 7.5The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of $9.4 \times 10^{3}\te…Preview

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Example 7.6Weighing the Earth: You are given the following data: $g = 9.81\text{ m s}^{-2}$, $R_E = 6.37 \times 10^{6}\text{ m}$, the distance to the m…Preview

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Example 7.7Express the constant $k$ of Eq. (7.38) in days and kilometres. Given $k = 10^{-13}\text{ s}^{2}\text{ m}^{-3}$. The moon is at a distance of…Preview

7.10

Energy of an Orbiting Satellite

For a satellite in a circular orbit around the Earth, the total mechanical energy is the sum of its kinetic energy (due to its motion) and its gravitational potential energy (due to its position in Ea…

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Example 7.8A 400 kg satellite is in a circular orbit of radius $2R_E$ about the Earth. How much energy is required to transfer it to a circular orbit o…Preview

Summary

- Newton’s universal law of gravitation: every particle attracts every other particle with a force , where . - Acceleration due to gravity on Earth’s surface: .

Points to Ponder

1. When one object moves under the gravitational pull of another, two quantities stay constant: the total mechanical energy (kinetic plus potential) and the angular momentum.

Exercises

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Exemplar Problems

Higher-order thinking / exemplar-style practice problems.

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