This chapter covers the concept of gravitation and its significance in the universe, particularly the universal law of gravitation and its effects on objects on Earth and in space.
GRAVITATION – Formula & Equation Sheet
Essential formulas and equations from Science, tailored for Class 9 in Science.
This one-pager compiles key formulas and equations from the GRAVITATION chapter of Science. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
F = G * (Mm)/(d²)
F is the gravitational force (N), G is the gravitational constant (6.67 × 10⁻¹¹ N m²/kg²), M and m are the masses of the two objects (kg), and d is the distance between their centers (m). This is the universal law of gravitation, explaining the attractive force between any two masses.
W = mg
W is the weight (N), m is the mass (kg), and g is the acceleration due to gravity (approximately 9.8 m/s² near the Earth's surface). This formula indicates that weight is the force exerted by gravity on an object.
g = GM/R²
g is the acceleration due to gravity (m/s²), G is the gravitational constant, M is the mass of the Earth (6 × 10²⁴ kg), and R is the radius of the Earth (6.4 × 10⁶ m). This formula calculates the gravitational acceleration at the surface of any celestial body.
F = ma
F is the net force (N), m is the mass (kg), and a is the acceleration (m/s²). This fundamental equation relates force, mass, and acceleration, applicable to any object in motion.
v = u + at
v is the final velocity (m/s), u is the initial velocity (m/s), a is the acceleration (m/s²), and t is the time (s). This equation is used in uniformly accelerated motion.
s = ut + 1/2 at²
s is the displacement (m), u is the initial velocity (m/s), a is the acceleration (m/s²), and t is the time (s). It provides the distance covered under uniform acceleration.
v² = u² + 2as
This relates final velocity (v), initial velocity (u), acceleration (a), and displacement (s). Useful for determining speeds and distances in motion problems.
W_m = (1/6)W_e
W_m is the weight of an object on the moon, and W_e is its weight on Earth. This formula shows that an object's weight is roughly one-sixth of its weight on Earth due to the moon's lower gravitational force.
P = F/A
P is pressure (Pa), F is force (N), and A is area (m²). This formula defines pressure as force applied per unit area, relevant in various physical scenarios.
V_f = V_i + a*t
V_f is final velocity, V_i is initial velocity, a is acceleration, and t is time. It is another version to understand motion under uniform acceleration.
Equations
F = G * (Mm)/(d²)
Fundamental formula for gravitational force. Ensure G is applied correctly.
g = GM/R²
Calculate local acceleration due to gravity. Important for understanding weight variation.
W = mg
Weight calculation vital to grasp force exerted by gravity.
v = u + at
Use for calculating final speed of a falling object under gravity.
s = ut + 1/2 at²
Necessary for assessing distance in vertically falling bodies.
v² = u² + 2as
Utilize for scenarios of height reached in free-fall or upward motions.
P = F/A
Relevant for any applications of thrust and area, especially in fluids.
W_m = (1/6)W_e
Compare weights between Earth and Moon for different objects.
g = 9.8 m/s²
General usage of g for Earth unless specified otherwise.
F = ma
General relationship for any forces acting upon objects.
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