Gravitation-D-MCQ

Acceleration is a vector quantity, which means it has both magnitude and direction. When we talk about positive acceleration, we mean that the acceleration is acting in the same direction as the motion of the object. For example, when a car speeds up while moving forward, its acceleration is in the forward direction, which is the same as its motion. This causes the speed of the object to increase. In physics, we choose a positive direction (usually the direction of motion) and then assign signs to other quantities based on whether they act in that direction or opposite to it. If acceleration acts opposite to motion, we call it negative acceleration or retardation, which causes the object to slow down.

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When we drop a paper and a stone from the same height, the stone reaches the ground first because the paper experiences more air resistance. Air resistance is a frictional force exerted by air on objects moving through it. The paper has a larger surface area and very less mass compared to the stone, so the upward air resistance force has a greater effect on the paper, slowing it down significantly. However, if this experiment is performed in a vacuum (where there is no air), both the paper and the stone would fall at exactly the same rate because gravity acts equally on all objects regardless of their mass. This was famously demonstrated by Galileo and later by astronauts on the Moon. So the slower fall of paper is not due to gravity or mass difference, but due to air resistance.

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Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. The gravitational force between two objects becomes weaker as the distance between them increases and becomes zero only at infinite distance. Therefore, scientists define the gravitational potential energy of an object to be zero when it is at an infinite distance from the Earth. As the object comes closer to the Earth, it loses potential energy, which gets converted into kinetic energy. At the Earth’s surface, the gravitational potential energy is negative (below zero) because work must be done to move the object away from the Earth against gravity. This convention makes the mathematics of gravitation simpler and more consistent.

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According to popular legend, the Italian scientist Galileo Galilei demonstrated that objects of different masses fall at the same rate by dropping two balls of different weights from the top of the Leaning Tower of Pisa. He did this to challenge the ancient belief of Aristotle that heavier objects fall faster than lighter ones. Although historians debate whether Galileo actually performed this exact experiment, it is a famous story that represents his revolutionary approach to science—using experiments rather than just philosophical arguments. Galileo’s work on free fall was crucial because it showed that in the absence of air resistance, all objects fall with the same acceleration due to gravity, regardless of their mass. This was a major step in the development of physics and later influenced Newton’s work on gravitation.

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According to Newton’s universal law of gravitation, the gravitational force between two objects is inversely proportional to the square of the distance between their centres. This means F ∝ 1/d². If the distance is tripled (becomes 3 times the original distance), then the new force becomes F_new = F_original × (1/3²) = F_original × 1/9. So the gravitational force becomes one-ninth of the original force. This is called the inverse-square law, and it is a fundamental property of gravity. It means that as objects move farther apart, the gravitational pull between them decreases very rapidly. For example, if you double the distance, the force becomes one-fourth; if you triple it, it becomes one-ninth, and so on.

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Although Newton formulated the universal law of gravitation and gave the formula F = GMm/d², he did not know the exact value of G (the universal gravitational constant). It was Henry Cavendish, a British scientist, who first measured the value of G in 1798, more than 100 years after Newton’s work. Cavendish used a very sensitive instrument called a torsion balance to measure the tiny gravitational force between two lead spheres. His experiment is often called “weighing the Earth” because knowing G allowed scientists to calculate the mass of the Earth. Cavendish’s value of G was remarkably accurate for his time. The currently accepted value of G is 6.67 × 10⁻¹¹ N·m²/kg². This experiment is considered one of the most important in physics because it provided the first direct measurement of gravitational force between ordinary objects.

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The acceleration due to gravity (g) is not constant everywhere. It depends on the distance from the Earth’s centre. The formula for g at a distance r from the Earth’s centre is g = GM/r², where M is the mass of the Earth and G is the universal gravitational constant. As we go higher above the Earth’s surface, the value of r increases, so g decreases. This means that at the top of a high mountain, the value of g is slightly less than at sea level. The decrease is small for normal heights but becomes significant at very high altitudes, such as in satellites or at the International Space Station. At the equator, g is also slightly smaller than at the poles due to the Earth’s rotation and its shape. Understanding this variation is important for many applications, including satellite motion and high-altitude physics.

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Weight is the gravitational force exerted by the Earth on an object. It is the force with which the Earth attracts the object towards its centre. Weight is a force, which means it is a vector quantity having both magnitude and direction (always directed towards the centre of the Earth). The formula for weight is W = mg, where m is the mass of the object and g is the acceleration due to gravity. Weight depends on both mass and the value of g at that location. For example, the weight of an object on the Moon is about one-sixth of its weight on Earth because the Moon’s gravity is weaker. It is important to remember that weight is different from mass—mass is the amount of matter in an object and remains constant, while weight can change depending on the gravitational field.

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The universal gravitational constant G is a fundamental constant of nature. Its accepted value is 6.67 × 10⁻¹¹ N·m²/kg², which is approximately 6.7 × 10⁻¹¹ N·m²/kg² for most calculations. This is an extremely small number, which shows that gravity is a very weak force compared to other forces like electromagnetic force. The units of G are N·m²/kg², which can be derived from the formula F = GMm/d². By rearranging, we get G = Fd²/(Mm), giving these units. The small value of G means that the gravitational force between everyday objects is negligible. It becomes significant only when at least one of the objects has a very large mass, like a planet or a star. G is called “universal” because it has the same value everywhere in the universe.

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Weight is given by the formula W = mg. For a given location, the value of g is constant. Therefore, weight is directly proportional to mass. This means that if the mass of an object doubles, its weight also doubles. If the mass becomes half, the weight also becomes half. This direct proportionality is the reason why we often use weight and mass interchangeably in everyday language, though scientifically they are different concepts. Weight depends on mass and gravity, while mass is a measure of the amount of matter and remains constant everywhere. The weight of an object does not depend on its shape, volume, or density—only on its mass and the gravitational field it is in. For example, a 10 kg object has a weight of about 98 N on Earth but only about 16 N on the Moon, while its mass remains 10 kg.

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In physics, when studying motion, we use specific symbols to represent different quantities to make equations easier to understand. The distance travelled by an object is represented by the symbol ‘s’. This comes from the Latin word “spatium” which means space or distance. Other common symbols are: ‘u’ for initial velocity, ‘v’ for final velocity, ‘a’ for acceleration, and ‘t’ for time. It is important to remember these symbols because they appear in all the equations of motion. For example, the equation s = ut + ½at² uses ‘s’ for distance, ‘u’ for initial velocity, ‘a’ for acceleration, and ‘t’ for time. Using consistent symbols helps us communicate physics concepts clearly and solve problems systematically.

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The standard value of acceleration due to gravity on Earth’s surface is 9.8 m/s². This means that if you drop an object from rest, its speed increases by 9.8 metres per second every second. In the first second, it reaches a speed of 9.8 m/s; in the second second, its speed becomes 19.6 m/s; and so on (ignoring air resistance). This value varies slightly depending on location—it is slightly less at the equator and slightly more at the poles—but for most calculations in school physics, we use 9.8 m/s². Sometimes, to make calculations simpler, we use 10 m/s² as an approximation. The value of g was first measured accurately by scientists like Galileo and later refined by others. It is one of the most important constants in physics.

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Weight is a force, and force is a vector quantity. This means that weight has both magnitude and direction. The magnitude of weight is given by W = mg, and its direction is always towards the centre of the Earth (downward). In physics, a vector quantity requires both a numerical value (magnitude) and a direction to be fully described. For example, saying “an object has a weight of 50 N” gives the magnitude, but to completely describe the weight, we must also say it acts “downward.” This is different from scalar quantities like mass, temperature, or speed, which only have magnitude and no direction. Understanding the vector nature of weight is important when analyzing forces acting on objects, especially when multiple forces are involved.

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Gravitational acceleration (g) is the acceleration experienced by an object due to the Earth’s gravitational pull. It always acts towards the centre of the Earth. This is because the Earth’s gravitational force pulls every object towards its centre. This direction is what we commonly call “downward” or “vertical.” It is important to understand that this direction is the same regardless of where you are on Earth—whether at the North Pole, the equator, or anywhere in between, the gravitational acceleration points towards the centre of the Earth. This constant direction is what makes objects fall straight down when dropped. The word “down” is simply our way of describing the direction towards the Earth’s centre.

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Mass is a fundamental property of matter. It is the measure of the amount of matter present in an object. Unlike weight, mass does not change with location. Whether the object is on Earth, on the Moon, in space, or on any other planet, its mass remains exactly the same. For example, a 10 kg object has a mass of 10 kg everywhere in the universe. What changes is its weight because weight depends on the gravitational field. On the Moon, the same object weighs only about 1/6 of its weight on Earth, but its mass is still 10 kg. Mass is also a measure of inertia—the resistance of an object to changes in its state of motion. This property remains constant, which is why we say mass is an intrinsic property of matter.

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When we throw an object upward, we choose the upward direction as positive. In this case, the object’s initial velocity (u) is positive, and it is moving upward. However, the acceleration due to gravity (g) acts downward, towards the Earth’s centre. Since downward is opposite to the positive direction, the acceleration due to gravity is taken as negative. So we write a = -g when the object is moving upward. This negative acceleration causes the object to slow down as it moves upward. At the highest point, the velocity becomes zero, and then the object starts falling back down. During the downward motion, the acceleration is positive because it acts in the direction of motion. This sign convention is very important when solving numerical problems involving vertical motion.

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The acceleration due to gravity (g) on the surface of the Earth is approximately 9.8 m/s². This is the standard value used in physics. It means that in the absence of air resistance, the speed of a freely falling object increases by 9.8 m/s every second. This value is often rounded to 10 m/s² for simpler calculations in school problems. The value of g is not exactly the same everywhere on Earth—it varies slightly with altitude, latitude, and local geology—but 9.8 m/s² is the average value that is widely accepted. For comparison, the value of g on the Moon is only about 1.6 m/s², which is why objects weigh less there. The accurate value of g is important for many practical applications, from engineering to space exploration.

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At the exact centre of the Earth, the acceleration due to gravity is zero. This happens because the gravitational pull from all directions cancels out. If you were at the Earth’s centre, you would be pulled equally in all directions by the mass surrounding you, resulting in no net gravitational force and therefore no acceleration. As you move from the Earth’s surface towards the centre, the value of g gradually decreases. It is maximum at the surface and becomes zero at the centre. This is an important concept in understanding the Earth’s internal structure. The variation of g with depth is different from its variation with height—while g decreases with height above the surface, it also decreases as we go deeper into the Earth, reaching zero at the centre.

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The formula for acceleration due to gravity on the Earth’s surface is g = GM/R², where G is the universal gravitational constant, M is the mass of the Earth, and R is the radius of the Earth. If the mass M is doubled (becomes 2M) while the radius R remains unchanged, then the new value of g becomes g’ = G(2M)/R² = 2(GM/R²) = 2g. So the acceleration due to gravity would become double its original value. This means that if the Earth were twice as massive but the same size, everything would weigh twice as much. This relationship shows that g is directly proportional to the mass of the Earth when the radius is constant. Conversely, if the radius were doubled while mass remained constant, g would become one-fourth.

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Inertia is the property of an object that resists changes in its state of motion. Mass is the quantitative measure of inertia. This means that the more mass an object has, the more inertia it has. A heavier object is harder to move from rest, harder to stop once it is moving, and harder to change its direction. For example, a loaded truck has much more inertia than a bicycle, which is why it takes much more force to start or stop the truck. This relationship between mass and inertia is fundamental to Newton’s First Law of Motion (the law of inertia). Understanding this helps explain many everyday observations—why heavier objects are harder to push, why it takes longer to stop a heavy vehicle, and why a small force has little effect on a massive object.

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Acceleration due to gravity (g) is a type of acceleration, so its unit is the same as the unit of acceleration. The SI unit of acceleration is metres per second squared, written as m/s² or m s⁻². This unit tells us how much the velocity of an object changes per second. For example, g = 9.8 m/s² means that the velocity of a freely falling object increases by 9.8 metres per second every second. The unit m/s² can be understood as (m/s)/s—it is the change in velocity (m/s) divided by time (s). This is different from the unit of speed (m/s) or the unit of force (N). It is important to use the correct units when solving physics problems to avoid mistakes in calculations.

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The equation s = ut + ½at² is the second equation of motion. It gives the distance (s) travelled by an object moving with uniform acceleration (a) over a time (t), when its initial velocity is (u). The first term (ut) represents the distance the object would travel if it continued at its initial velocity, and the second term (½at²) represents the additional distance covered due to acceleration. This equation is very useful for solving problems involving motion. For example, it can tell us how far a car travels while speeding up, or how far a falling object drops in a certain time. It is important to remember that this equation is valid only when acceleration is constant or uniform.

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Acceleration due to gravity (g) is caused by the Earth’s gravitational attraction. The Earth pulls every object towards its centre with a force called weight (W = mg). This force causes the object to accelerate towards the Earth. The acceleration produced is what we call the acceleration due to gravity (g). It is important to understand that g is not caused by Earth’s rotation, magnetic field, or air pressure. It is a direct consequence of the gravitational force. The value of g depends on the mass of the Earth and the distance from its centre, as given by the formula g = GM/r². This gravitational force is what keeps us on the ground, makes objects fall, and governs the motion of the Moon and satellites.

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In the equations of motion, the final velocity of an object is represented by the symbol ‘v’. This is the velocity of the object at the end of the time interval being considered. The symbol ‘u’ represents the initial velocity (velocity at the start), ‘a’ represents acceleration, ‘s’ represents distance, and ‘t’ represents time. Using consistent symbols helps us communicate physics concepts clearly. For example, in the equation v = u + at, ‘v’ gives the final velocity after time ‘t’ when the object starts with initial velocity ‘u’ and accelerates at ‘a’. It is important to distinguish between initial and final velocity because many problems involve finding one from the other using the equations of motion.

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Air resistance is a type of frictional force that opposes the motion of an object as it moves through air. When an object moves through air, the air molecules collide with the object’s surface, creating a force that acts in the opposite direction to the motion. This force is called air resistance or drag. It depends on several factors: the speed of the object (faster objects experience more air resistance), the surface area of the object (larger area means more resistance), and the shape of the object (streamlined shapes experience less resistance). Air resistance is a form of fluid friction (since air is a fluid). In many physics problems, we ignore air resistance to simplify calculations, but in real life, it can significantly affect the motion of objects, especially at high speeds or for objects with large surface areas.

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In free fall, an object falls under the influence of gravity alone, with no air resistance. The acceleration due to gravity (g) is constant (approximately 9.8 m/s²). Since acceleration is constant, the velocity of the falling object increases uniformly. This means that the object gains equal amounts of speed in equal intervals of time. For example, in the first second, its speed increases from 0 to 9.8 m/s; in the next second, from 9.8 to 19.6 m/s; and so on. The relationship is given by the equation v = u + gt, where u is the initial velocity. If the object starts from rest (u = 0), then v = gt. This uniform increase in velocity is a characteristic of motion with constant acceleration.

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The weight of an object on the Moon is less than its weight on Earth because the Moon’s gravitational field is weaker than Earth’s. The acceleration due to gravity on the Moon is about 1.6 m/s², which is approximately one-sixth of the Earth’s g (9.8 m/s²). Since weight W = mg, and the mass of the object is the same on both the Earth and the Moon, the weight on the Moon is about one-sixth of the weight on Earth. For example, if an object weighs 60 N on Earth, it would weigh only about 10 N on the Moon. This is why astronauts on the Moon appear to bounce and move easily—they are lighter there. However, their mass remains the same. Understanding the difference between mass and weight is crucial for space exploration and physics.

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Acceleration is taken as negative when it acts in the opposite direction to the motion of the object. This is also called deceleration or retardation. For example, when a car applies brakes, the acceleration is in the opposite direction to the car’s motion, so we say the car is decelerating. In equations, we assign a negative sign to such acceleration. This convention helps us distinguish between speeding up (positive acceleration) and slowing down (negative acceleration). If we choose the direction of motion as positive, then acceleration in the same direction is positive, and acceleration in the opposite direction is negative. This sign convention is important for correctly solving problems involving motion, especially when dealing with stopping distances or objects thrown upward.

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A satellite orbiting very close to the Earth’s surface (at an altitude of about 200-400 km) takes approximately 90 minutes to complete one orbit around the Earth. This is known as the orbital period of a low Earth orbit satellite. The International Space Station (ISS), for example, orbits at about 400 km altitude and takes about 92 minutes to complete one orbit. This means that astronauts on the ISS experience about 16 sunrises and sunsets every day! This short orbital period is because the satellite is close to Earth, so the gravitational force is strong, requiring the satellite to move very fast (about 28,000 km/h) to stay in orbit. Geostationary satellites, on the other hand, orbit much farther away (about 36,000 km) and have an orbital period of 24 hours.

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One of the most important discoveries in physics is that acceleration during free fall is independent of the mass of the object. All objects, regardless of their mass, fall with the same acceleration (g = 9.8 m/s²) in the absence of air resistance. This means that a heavy object and a light object dropped from the same height will hit the ground at the same time (if air resistance is neglected). This was famously demonstrated by Galileo and is a consequence of the equivalence of gravitational mass and inertial mass. The acceleration depends on the gravitational field (which is determined by the mass and radius of the Earth and the distance from its centre) but not on the mass of the falling object. This principle is fundamental to our understanding of gravity.

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When an object is thrown upward, it moves against gravity and its velocity decreases until it reaches the highest point. At this point, the object momentarily stops before starting to fall back down. So at the maximum height, the velocity becomes zero. However, even though the velocity is zero, the acceleration due to gravity (g) is still acting downward with a magnitude of 9.8 m/s². This is because acceleration is the rate of change of velocity—at the instant of zero velocity, the velocity is about to change direction. This concept often confuses students: just because velocity is zero, it does not mean acceleration is zero. The object’s velocity becomes zero at the top, but gravity continues to act, which is why the object falls back down.

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Weight is a force, and the SI unit of force is the newton (N). Weight is calculated using the formula W = mg, where m is mass in kilograms and g is acceleration due to gravity in m/s². Multiplying kg × m/s² gives kg·m/s², which is defined as one newton (N). One newton is the force required to give a mass of 1 kilogram an acceleration of 1 m/s². So, for example, a 10 kg object has a weight of approximately 98 N on Earth (10 kg × 9.8 m/s² = 98 N). It is important to remember that weight and mass are different—mass is measured in kilograms, while weight is measured in newtons. Using the correct unit is essential in physics.

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Motion under gravity (such as free fall) is an example of uniform acceleration because the acceleration due to gravity (g) is constant near the Earth’s surface. This means that the velocity of the falling object changes by equal amounts in equal time intervals. The acceleration is uniform (constant) throughout the motion, regardless of the object’s mass. Even when an object is thrown upward, the acceleration (due to gravity) is constant and acts downward throughout the entire motion—during ascent, at the highest point, and during descent. The only change is that the velocity decreases during ascent (positive acceleration? Actually, acceleration is negative during ascent) and increases during descent, but the acceleration value itself remains constant. This is why the equations of motion (v = u + at, s = ut + ½at², and v² = u² + 2as) can be applied to motion under gravity by simply replacing a with g.

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In the equations of motion, the initial velocity of an object is represented by the symbol ‘u’. Initial velocity is the velocity at the start of the time interval being considered. For example, if a car starts from rest, its initial velocity u = 0. If a ball is thrown upward with a speed of 20 m/s, then u = 20 m/s (taking upward direction as positive). The symbol ‘v’ is used for final velocity, ‘a’ for acceleration, ‘s’ for distance, and ‘t’ for time. Using these standard symbols helps us write and solve physics equations consistently. The distinction between initial and final velocity is important because many problems ask us to find one from the other using the equations of motion.

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The equation v² = u² + 2as is the third equation of motion. It relates velocity (both initial velocity u and final velocity v) and distance (s). This equation does not involve time, which makes it very useful when time is not given in the problem. For example, if we know the initial velocity, final velocity, and acceleration of an object, we can find the distance it has travelled without needing to know how long it took. Similarly, we can find the final velocity if we know the initial velocity, acceleration, and distance. This equation is derived from the other two equations of motion and is widely used in problems involving stopping distances, projectile motion, and any situation where time is not known.

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The gravitational force acting on an object is called its weight. Weight is the force with which the Earth attracts an object towards its centre. It is given by the formula W = mg, where m is the mass of the object and g is the acceleration due to gravity. Weight is a force, which means it is a vector quantity (it has both magnitude and direction). The direction is always towards the centre of the Earth. This is different from mass, which is a measure of the amount of matter in an object and is a scalar quantity. Density is mass per unit volume, and inertia is the resistance to change in motion. So, weight is the correct term for the gravitational force acting on an object.

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The SI unit of mass is the kilogram (kg). Mass is a fundamental quantity in physics, and it measures the amount of matter in an object. The kilogram is one of the seven base units of the International System of Units. Other common units of mass include grams (g) and tonnes (t). It is important to distinguish between mass and weight: mass is measured in kilograms, while weight is measured in newtons. In everyday life, we often use the terms interchangeably, but in physics, they are different concepts. For example, an object with a mass of 10 kg has a weight of about 98 N on Earth, but its mass is still 10 kg on the Moon, where its weight would be only about 16 N.

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During free fall near the Earth’s surface, the acceleration is constant (assuming air resistance is neglected). This constant acceleration is the acceleration due to gravity (g = 9.8 m/s²). It does not change with time or with the mass of the falling object. The velocity of the object increases uniformly, but the acceleration remains constant. This is what makes free fall an example of uniformly accelerated motion. The constancy of g allows us to use the equations of motion (v = u + gt, s = ut + ½gt², and v² = u² + 2gs) to solve problems involving falling objects. At higher altitudes, g is slightly less, but for most practical purposes near the Earth’s surface, we treat it as constant.

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The equation v = u + at is the first equation of motion. It represents the velocity-time relation, which means it shows how the velocity of an object changes with time under uniform acceleration. In this equation, ‘v’ is the final velocity, ‘u’ is the initial velocity, ‘a’ is the constant acceleration, and ‘t’ is the time. This equation tells us that the final velocity is equal to the initial velocity plus the product of acceleration and time. This is very useful for finding the velocity of an object after a certain time when it accelerates uniformly. For example, if a car starts from rest (u = 0) and accelerates at 2 m/s² for 5 seconds, its velocity after 5 seconds is v = 0 + 2 × 5 = 10 m/s.

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Free fall is defined as the motion of an object when only the force of gravity is acting on it. This means that air resistance and all other forces are neglected. In free fall, the object accelerates downward with acceleration equal to g (the acceleration due to gravity). This is why all objects in free fall fall with the same acceleration, regardless of their mass. In reality, air resistance always acts on falling objects, so true free fall only occurs in a vacuum or in situations where air resistance is negligible. The concept of free fall is very important in physics because it allows us to study the effects of gravity without the complication of other forces. Examples of free fall include a dropped ball (ignoring air resistance) and the motion of astronauts in orbit (who are in free fall around the Earth).

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The mass of the Earth is approximately 6 × 10²⁴ kg. This is a very large number, which is why the gravitational force of the Earth is so strong. Knowing the mass of the Earth is essential for calculating the gravitational force between the Earth and other objects, and for determining the value of g. The mass of the Earth was first calculated after Cavendish determined the value of G. By rearranging the formula g = GM/R², we can solve for M = gR²/G. Using the known values of g (9.8 m/s²), R (6.4 × 10⁶ m), and G (6.67 × 10⁻¹¹), we get the mass of the Earth. This calculation is one of the most important applications of Newton’s law of gravitation.

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Mass is a measure of the amount of matter in an object, and it is also the measure of its inertia. Inertia is the property of an object that resists changes in its state of motion. The greater the mass of an object, the greater its inertia, and the harder it is to start moving, stop moving, or change its direction. This is why a heavy object like a truck is harder to push than a light object like a bicycle. Mass is also used to calculate weight (W = mg) and is a fundamental property of matter. Unlike volume (space occupied), density (mass per unit volume), or weight (force of gravity on an object), mass is an intrinsic property that does not change with location. Understanding that mass measures inertia is crucial for understanding Newton’s First Law of Motion.

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Near the Earth’s surface, the acceleration due to gravity (g) is considered constant for most practical purposes. The value of g is approximately 9.8 m/s². Although g actually varies slightly with altitude and latitude, the variation is small enough that we can treat it as constant for solving school-level problems. This constancy is what allows us to use the equations of motion (v = u + at, s = ut + ½at², and v² = u² + 2as) with a = g. In many problems, g is even rounded to 10 m/s² to simplify calculations. However, for very high altitudes or very precise calculations, the variation of g must be taken into account. For example, at the top of Mount Everest (about 8,848 m), the value of g is slightly less than at sea level.

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Weight is the gravitational force acting on an object, and it is calculated using the formula W = mg. Here, ‘m’ is the mass of the object (in kilograms) and ‘g’ is the acceleration due to gravity (in m/s²). Weight is measured in newtons (N). This formula shows that weight is directly proportional to mass—the more mass an object has, the greater its weight. It also shows that weight depends on g, which varies with location. For example, on the Moon where g is 1.6 m/s², the weight of the same object is much less than on Earth where g is 9.8 m/s². The formula W = mg is derived from Newton’s second law of motion, F = ma, where the force F is the weight and the acceleration a is g.

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Free fall is the motion of an object where the only force acting on it is gravity. This means that all other forces, such as air resistance, friction, and magnetic forces, are ignored. In free fall, the object accelerates at the rate of g (the acceleration due to gravity). This is a special case of motion because the acceleration is constant and independent of the mass of the object. Examples of free fall include a ball dropped from a height (ignoring air resistance) and an astronaut in a spacecraft orbiting the Earth (who is in continuous free fall). Free fall is not limited to objects falling downward—an object thrown upward is also in free fall (with gravity acting downward) during its entire flight, from the moment it leaves the hand until it hits the ground.

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The weight of an object depends on two factors: its mass (m) and the acceleration due to gravity (g) at its location. The formula W = mg shows that weight is the product of mass and gravity. If the mass of an object increases, its weight increases. If the gravity increases (for example, on a planet with stronger gravity), the weight also increases. However, mass alone does not determine weight because g varies from place to place. For example, a person with a mass of 60 kg has a weight of about 588 N on Earth, but only about 96 N on the Moon. The person’s mass (60 kg) is the same in both places, but the gravity is different, so the weight changes. This is why weight depends on both mass and gravity.

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In the absence of air (in a vacuum), a paper and a stone will fall at the same rate. This is because gravity acts equally on all objects regardless of their mass, shape, or size. When there is no air resistance, the only force acting on the objects is gravity, and both experience the same acceleration (g). This was famously demonstrated by Galileo and later by astronaut David Scott on the Moon during the Apollo 15 mission, who dropped a feather and a hammer, and both hit the ground at the same time. On Earth, we see a difference because air resistance affects light objects with large surface areas (like paper) more than heavy, compact objects (like a stone). But without air, the difference disappears.

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The radius of the Earth is approximately 6.4 × 10⁶ metres (or 6400 kilometres). This value is essential for many calculations in physics, especially those involving gravitation and satellite motion. The Earth is not a perfect sphere—it is slightly flattened at the poles and bulges at the equator—so the radius varies slightly. The average radius is about 6.37 × 10⁶ m, but 6.4 × 10⁶ m is a commonly used approximation. Knowing the Earth’s radius allows us to calculate the value of g, the escape velocity, the orbital period of satellites, and many other important physical quantities. For example, we use the radius to calculate the mass of the Earth from the formula g = GM/R².

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The acceleration due to gravity is denoted by the symbol ‘g’. This is a standard symbol used in physics all over the world. The value of g on the Earth’s surface is approximately 9.8 m/s². It is important to distinguish between ‘g’ and ‘G’—’g’ is the acceleration due to gravity (which varies with location), while ‘G’ is the universal gravitational constant (which has a fixed value of 6.67 × 10⁻¹¹ N·m²/kg²). In equations of motion under gravity, we replace ‘a’ (acceleration) with ‘g’. For example, the equations become v = u + gt, s = ut + ½gt², and v² = u² + 2gs. Understanding the difference between g and G is crucial for solving gravitation problems correctly.

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Near the Earth’s surface, when an object is in motion under the influence of gravity alone, we replace the general acceleration ‘a’ in the equations of motion with ‘g’, the acceleration due to gravity. This is because the object is experiencing a constant acceleration due to gravity. So the equations of motion become: v = u + gt, s = ut + ½gt², and v² = u² + 2gs. Here, ‘g’ is positive when the object is falling downward (taking downward as positive) and negative when the object is moving upward (taking upward as positive). This substitution is valid as long as we ignore air resistance and assume the motion is near the Earth’s surface where g is constant. These modified equations are used to solve all problems involving vertical motion under gravity, such as free fall and upward projection.Close