Mind Map: Gravitation (Class IX - NCERT)
Every object in the universe attracts every other object with a force.
\[ F = \frac{G m_1 m_2}{r^2} \]
where,
- \( F \) = Gravitational force
- \( G \) = Universal Gravitational Constant (\( 6.674 \times 10^{-11} \) Nm²/kg²)
- \( m_1, m_2 \) = Masses of two objects
- \( r \) = Distance between the objects
When an object falls under the influence of gravity alone.
\[ g = \frac{GM}{R^2} \]
where,
- \( M \) = Mass of Earth
- \( R \) = Radius of Earth
Standard value: \( g = 9.8 \) m/s² near Earth's surface.
Equations of Motion under Gravity:
\[ v = u + gt \]
\[ s = ut + \frac{1}{2} gt^2 \]
\[ v^2 = u^2 + 2gs \]
If object is thrown upward, \( g \) is taken as negative.
Mass (\( m \)): Amount of matter in an object (constant everywhere).
Weight (\( W \)): Force due to gravity on an object.
\[ W = mg \]
Weight varies with location due to change in \( g \).
Gravity on Moon is \( \frac{1}{6} \)th of Earth's gravity.
\[ W_{\text{Moon}} = \frac{1}{6} W_{\text{Earth}} \]
Thrust: Force applied perpendicular to a surface.
Pressure:
\[ P = \frac{\text{Force}}{\text{Area}} \]
SI unit: Pascal (Pa).
Pressure decreases with increase in surface area.
Buoyant Force: Upward force exerted by a fluid.
Archimedes' Principle:
A body immersed in a fluid experiences a buoyant force equal to the weight of the fluid displaced by it.
Definition: Ratio of the density of a substance to the density of water.
\[ \text{Relative Density} = \frac{\text{Density of Substance}}{\text{Density of Water}} \]
No unit (since it is a ratio).
Please don not use wrong word