Questions
5 questions per paper
Difficulty
Medium
Importance
Core - never skip
Overview
Gravitation governs the motion of celestial bodies and the fundamental interaction of mass in the universe. Mastery of this topic is essential for both competitive exams and board physics, as it integrates core mechanics with fluid dynamics through buoyancy concepts.
Universal Law of Gravitation
Newton's law dictates that every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This is the cornerstone of orbital mechanics and gravitational field calculations.
- F = G(M*m)/r^2
- G (Universal Gravitational Constant) = 6.673 x 10^-11 Nm^2/kg^2
- The force is always attractive and acts along the line joining the centers of the two bodies.
- The inverse square law implies force decreases rapidly as distance increases.
Free Fall and Acceleration due to Gravity
When an object moves under the sole influence of Earth's gravitational pull, it experiences a constant acceleration denoted by 'g'. Understanding the equations of motion under gravity is critical for solving kinematics problems involving vertical projectiles.
- g = GM/R^2
- Average value of g on Earth is 9.8 m/s^2
- Weight (W) = mg
- Equations of motion: v = u + gt, h = ut + 0.5gt^2, v^2 = u^2 + 2gh
- Mass remains constant, but weight varies based on the local value of g.
Thrust and Pressure
Thrust is the force acting perpendicularly on a surface, while pressure is defined as thrust per unit area. These concepts are fundamental in understanding fluid statics and how force distribution affects mechanical stress.
- Thrust = Force (F)
- Pressure (P) = Thrust/Area (A)
- SI Unit of Pressure is Pascal (Pa) or N/m^2
- Liquids exert pressure in all directions and increase with depth (P = h*rho*g).
Archimedes' Principle and Buoyancy
Archimedes' principle states that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid displaced by the body. This is the governing principle behind why objects float or sink in different media.
- Buoyant Force = Weight of fluid displaced
- Object floats if Density of object < Density of fluid
- Relative Density = Density of substance / Density of water
- Relative Density has no units as it is a ratio.
Formula Sheet
F = G(M*m)/r^2
g = GM/R^2
W = mg
P = F/A
P = h*rho*g
Relative Density = Density of substance / Density of water
v = u + gt
h = ut + 0.5gt^2
v^2 = u^2 + 2gh
Exam Tip
Always draw a free-body diagram for buoyancy problems and explicitly define the sign convention for vertical motion to avoid errors in displacement and velocity calculations.
Common Mistakes
- Confusing the constant 'G' (Universal Gravitational Constant) with 'g' (acceleration due to gravity).
- Failing to convert units (e.g., using cm or km instead of SI units like meters and kilograms) during complex numerical calculations.
- Neglecting to account for the direction of velocity and acceleration signs (using g as positive when the object is moving upward).
More Revision Notes
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