NCERT Solutions Class 11 Physics Chapter 7 – Gravitation

NCERT Solutions for Class 11 Physics Chapter 7 (Gravitation) explore the universal force that holds the universe together. From the falling of an apple to the orbits of planets and the behavior of black holes, gravitation is the fundamental force that governs large-scale structures in the cosmos. This chapter builds on the historical transition from the geocentric model to the heliocentric model, solidified by the mathematical brilliance of Johannes Kepler and Isaac Newton.

The NCERT Solutions for Class 11 Physics Chapter 7 by ALLEN are prepared by expert faculty to explain gravitational laws, orbital motion, and satellite dynamics with clarity. The solutions follow a structured, problem-solving approach aligned with JEE and NEET exam patterns.

For students preparing for JEE and NEET, Gravitation is a high-scoring chapter as it shares many mathematical similarities with Electrostatics. These solutions provide a clear path to understanding how the strength of gravity changes with height and depth, and what it takes for a satellite to stay in orbit.

1.0Class 11 Physics Chapter 7 : Key Concepts

This chapter examines the nature of gravitational interaction and its effects on celestial and terrestrial bodies. Key lessons include:

Kepler’s Laws of Planetary Motion:

• Law of Orbits: Planets move in elliptical orbits with the Sun at one focus.
• Law of Areas: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
• Law of Periods: The square of the time period of a planet is proportional to the cube of the semi-major axis of its orbit $(T^2\propto R^3).$
• Universal Law of Gravitation: Every particle in the universe attracts every other particle with a force:$F=G\frac{m_1{m}_2}{r^2}$
• The Gravitational Constant (G): Understanding the Cavendish experiment used to determine the value of $G\approx 6.67\times 10^{-11}{\text{ N m}}^2/{\text{kg}}^2.$

Acceleration due to Gravity (g):

• Relation with G: $g=\frac{GM}{R^2}$
• Variation of g with Altitude (h): g decreases as we go up.
• Variation of g with Depth (d): g decreases as we go down toward the center of the Earth.
• Gravitational Potential Energy: The work done in bringing a mass from infinity to a point $(U=-\frac{GMm}{r}).$
• Escape Speed ($v_e$): The minimum speed required for an object to break free from Earth's gravitational pull is called escape speeed/velocity. $(v_e=\sqrt{\frac{2GM}{R}}\approx 11.2\text{ km/s}).$

Earth Satellites:

• Orbital Speed ($v_o$): The speed required to keep a satellite in a circular orbit $(v_o=\sqrt{\frac{GM}{r}}).$
• Geostationary Satellites: Satellites that appear fixed over a point on Earth (Period = 24 hours).
• Polar Satellites: Satellites that orbit in a north-south direction for weather and environmental monitoring.
• Weightlessness: Understanding why astronauts feel "weightless" in a state of free fall while orbiting the Earth.

2.0Key Features of NCERT Solutions for Class 11 Physics Chapter 7

• Strong Mathematical Analogy for Better Retention: The solutions highlight clear parallels between gravitational and electrostatic formulas, helping students draw analogies between force laws, field concepts, and potential energy expressions for easier understanding and memorization.
• Clear Energy Analysis of Satellite Motion: A systematic breakdown of the total mechanical energy of a satellite, E = K + U,
  is provided, with logical explanations showing why the total energy of a bound gravitational system is always negative.
• Step-by-Step Derivation of Kepler’s Laws: Kepler’s Third Law is derived in a structured manner using Newton’s Law of Gravitation, enabling students to understand the physical reasoning behind planetary motion rather than memorizing results.
• Accurate Treatment of Variation in g: Detailed derivations explain how acceleration due to gravity varies with height and depth, including simplified expressions for the case h ≪ R (near Earth’s surface), reducing errors in approximation-based questions.
• Prepared by Expert Faculty: These NCERT Solutions are prepared by ALLEN subject experts, ensuring conceptual accuracy, mathematical rigor, and strict alignment with the latest NCERT syllabus.
• Exam-Oriented and Concept-Driven Explanations: All concepts are presented with proper assumptions, diagrams, and stepwise logic, making them highly effective for CBSE board exams and competitive exams like JEE and NEET.
• Complete Coverage of NCERT Exercises: Every example and exercise from NCERT Class 11 Physics Chapter 7 is solved in detail to help students master gravitation with confidence.