NEET Physics: Waves – NCERT Masterclass & 100 MCQ Quiz

GRAVITATION: NCERT MASTERCLASS

Complete NCERT Study Notes & 5-Part Mega Quiz for NEET

1. Kepler's Laws of Planetary Motion

Johannes Kepler formulated three empirical laws describing the motion of planets around the sun:

• Law of Orbits: All planets move in elliptical orbits with the Sun situated at one of the foci.
• Law of Areas: The line that joins any planet to the sun sweeps equal areas in equal intervals of time. This law is a consequence of the conservation of angular momentum.
• Law of Periods: The square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet.

$$T^2 \propto R^3$$

2. Universal Law of Gravitation

Newton's law states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

$$F = G \frac{m_1 m_2}{r^2}$$

Where $G = 6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2$ is the Universal Gravitational Constant. Gravity is a conservative, central, and always attractive force.

3. Acceleration Due to Gravity ($g$)

The acceleration experienced by a freely falling body due to the gravitational force of the Earth is called acceleration due to gravity ($g$). On the surface of the Earth, $g = \frac{GM}{R^2} \approx 9.8 \text{ m/s}^2$.

Variation of $g$:

• With Height ($h$): $g_h = g \left(1 - \frac{2h}{R}\right)$ (for $h \ll R$)
• With Depth ($d$): $g_d = g \left(1 - \frac{d}{R}\right)$. The value of $g$ becomes zero at the centre of the Earth.

4. Gravitational Potential Energy & Escape Speed

Gravitational Potential Energy ($U$): The work done in bringing a mass from infinity to a point in the gravitational field. $U = - \frac{GMm}{r}$. It is always negative.

Escape Speed ($v_e$): The minimum speed required for an object to escape from the gravitational influence of the earth. It is independent of the mass of the projectile.
$$v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR} \approx 11.2 \text{ km/s}$$

5. Earth Satellites & Energy

Orbital Speed ($v_o$): The velocity required to put a satellite into its orbit. $v_o = \sqrt{\frac{GM}{r}}$. Notice that $v_e = \sqrt{2} v_o$.

Energy of an Orbiting Satellite:

• Kinetic Energy ($K$) = $+ \frac{GMm}{2r}$
• Potential Energy ($U$) = $- \frac{GMm}{r}$
• Total Energy ($E$) = $- \frac{GMm}{2r}$ (The negative sign indicates that the satellite is bound to the Earth).

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🚀 NEET GRAVITATION MEGA QUIZ (100 MCQ)

Solve the 5 parts below to master Gravity, Escape Velocity, and Satellites.

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