CBSE Class 9 Physics Gravitation Notes Set 08

Gravitation and the Law of Gravitation

Every object in the universe attracts every other object. This force of attraction is called gravitation. The pull of the earth on a body is called gravity.
Newton's law: \( F = \dfrac{G m_1 m_2}{r^2} \). The force is proportional to the product of the masses and inversely proportional to the square of the distance. The value of \( G \) is \( 6.67\times10^{-11} \) N m² kg⁻² and it is the same everywhere in the universe.
The two bodies pull each other with equal and opposite forces, and the force does not depend on the medium between them.

Acceleration Due to Gravity

The acceleration produced in a freely falling body is \( g = \dfrac{GM}{R^2} \). Its value near the earth is 9.8 m/s². It does not depend on the mass of the falling body, so a heavy and a light body fall together in vacuum.
Weight is the force with which the earth attracts a body, \( W = mg \). Mass is the quantity of matter and does not change from place to place, but weight does. On the moon, g is about one-sixth of its value on the earth.

Variation of g

Satellites

A satellite stays in orbit because the gravitational pull supplies the centripetal force. For a circular orbit of radius r, the orbital speed is \( v = \sqrt{GM/r} \), which falls as the orbit gets larger. Kepler's third law gives \( T^2 \propto r^3 \).
A geostationary satellite has a period of 24 h, revolves about the earth's polar axis and appears fixed over one point of the earth.
The escape speed from the earth's surface is about 11.2 km/s. The speed of a satellite close to the earth is about 7.9 km/s. Objects inside a satellite appear weightless because they are in free fall along with it.

Free Fall Equations

For free fall from rest: \( v = gt \), \( h = \tfrac{1}{2}gt^2 \), \( v^2 = 2gh \). For a body thrown upward with speed u, the maximum height is \( u^2/2g \) and the time to reach it is \( u/g \).