NCERT Solutions for Class 9 science chapter 10 Gravitation are provided here. Students can refer to them while preparing and studying the chapter. These solutions can also be beneficial while revising the content before their exams. Class 9 chapter 10 science is an essential part of physics that covers the most basic concepts of gravitation on earth and the moon. It also explains how the terms mass and weight are different.
1. Introduction
2. Newton’s Law of Gravitation
3. Free Fall
4. Mass and Weight
5. Thrust and Pressure
Gravity is the force that causes bodies to attract each other with force proportional to their masses, and inversely proportional to the square of the distance between them.
The force that every body of matter — from the smallest atom to the largest star —constantly exerts on every other body of matter is called gravitation.
For example, the earth attracts a stone toward its centre. The moon is attracted towards the earth and revolves around it; the earth is attracted to the sun and revolves around it; all the planets are attracted towards the sun and revolve around it. The sun, with all of its planetary bodies, is attracted towards other bodies, which are, in turn, attracted toward still others, and so on indefinitely.
Centripetal force makes a body follow a curved path: its direction is always perpendicular to the velocity of the body, toward the fixed point, that is, the centre of curvature of the path.
Newton's law of universal gravitation, sometimes called the universal law of gravitation, states that every point mass in the universe is attracted to every other point mass with force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. It also states that this force acts along a straight line connecting the two points. This law is an example of the inverse-square law.
There are no exceptions; all objects exert some gravitational force and experience gravitational force from other objects, even though they may be too small or far away for us to detect.
Mathematically, this is expressed as:
F∝m1xm2
F∝1/d^2
F∝m1xm2/d^2
F=Gm1xm2/d^2
Here, F is the magnitude of the force, m1 is the first mass, m2 is the second mass, d is the distance between both bodies, and G is a constant with an approximate value of 6.674×10−11 Nm2/kg2 (N stands for newtons, m for metres, kg for kilograms).
The universal law of gravitation explains various phenomena which were previously supposed to be unconnected with each other. However, they are governed by the same rule. These phenomena are as follows:
The force that binds us to earth.
The motion of the moon around the earth.
The motion of planets around the sun.
The pull of the moon and sun cause tides.
Kepler’s Laws
Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the sun.
The planet revolves around the sun in an elliptical orbit, with the sun at one of its foci.
Area swept off by the planet during earth’s revolution is equal for equal intervals of time.
The square of the orbital period of a planet is proportional to the cube of the radius of the orbit.
Free Fall
Free-fall occurs when some object falls under the sole influence of gravity, and therefore its path is described by the equations of motion for a freely falling body.
Newton's law predicts that all objects should behave the same way during free fall, whether they are falling in the air or through space; all objects should accelerate at exactly 9.8 metres per second squared. This is the value of acceleration due to gravity on earth.
Gravity accelerates all objects at the same rate, regardless of their mass. Newton called this acceleration due to gravity and measured its value.
g = 9.8 m/s^2
We know that
F=Gm1xm2/d^2
Where F is the force applied by one object on another.
We also know that F = ma.
However, in the case of the earth, the equation will change to F = mg.
Thus,
GMxm/d^2 = mg.
Here, M represents the mass of the earth, and m represents the object's mass.
We get,
GM/d^2 = g.
This equation gives the relationship between G and g. Through this equation, the value of g on earth was calculated to be 9.8 m/s^2.
Since the earth is not a perfect sphere, its radius changes in different locations, such as the equator and poles; thus, the value of g changes. 9.8 is an average value.
Under the influence of the earth’s gravitational force, the acceleration changes from a to g, and the displacement changes from s to h (height). The equations of motion thus become:
v = u + gt
h = ut + ½ gt^2
v^2 = u^2 + 2gh.
Mass is a property of matter. The mass of an object's matter makes it hard to accelerate: when pushing on an object with a given force, the harder it is to move, the more mass it has.
Weight is a measure of force: more precisely, it is the amount of force needed to keep an object from falling due to gravity (or keep it moving in a straight line at constant speed if you are moving horizontally).
Thus, mass is an inherent property of an object; whereas, weight is the force applied by the earth on the object.
Mass is measured in kg, and weight is measured in newton as a force. One can state that the mass of an object remains the same all over the universe, whereas weight keeps changing.
Weight is given by the following formula:
W = mg
Where m is the mass of the object and g is the acceleration due to gravity.
The weight of an object is the force applied to it. The force applied will be much less on the moon, as it has a lesser mass than earth and a shorter radius.
The weight of an object on the moon will be given by:
W = G M m/r^2
Where W represents the weight of an object on the moon, G is the universal constant of gravity, M is the moon's mass, m is the mass of the object, and r is the moon's radius.
The weight of an object on the moon is one-sixth of the weight of that object on earth. For example, if an object weighs 60 N here on earth, it will experience a force of 10 N on the moon.
Newton's third law of motion describes thrust. The force applied on a surface in a direction perpendicular to the surface is called thrust.
The simplest example of this principle is a rocket being launched into space. As the rocket fuel burns, it emits high-temperature gas, which is accelerated backwards out of the engine nozzle at extremely high speed; this provides an equal and opposite forward thrust force on the rocket, accelerating it forwards and upwards. The same principle applies to the reaction of a propeller blade or impeller in water or air, or any fluid.
Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Pressure is distributed equally against all surfaces in contact with a fluid, making it possible to calculate the pressure of any given point (or region) within that fluid, provided the point (or region) is not moving relative to that surface. It follows from the above equations that any change in the volume of an enclosed static fluid will be accompanied by a change in pressure proportional to its change in volume.
Fluid pressure is a quantity much like temperature or density. It is defined as the force per unit area acting on an object. The SI unit for pressure is the pascal (Pa).
Buoyancy is a force exerted by a fluid that opposes an object's weight. The resulting force on the object causes it to float or sink.
The concept of buoyancy is important for determining whether an object will float in water or some other liquid or, if it sinks, how fast it will do so. Buoyancy is affected by several factors, including the density and shape of the object, the density of the fluid and the volume of fluid displaced.
Archimedes’ principle states that any body partially or fully immersed in fluid experiences an upward force equal to the weight of the fluid it displaces.
Archimedes’ principle is important because everything from ships to submarines, and even hot air balloons, is designed to work on this principle.
The three equations of motion for a body in a free fall are as follows:
v = u + gt
h = ut + ½ gt^2
v^2 = u^2 + 2gh
Gravitational force is the attractive force applied by any object with a mass on every other object.
The universal law of gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
G is the universal constant of gravitation, whereas g is the acceleration due to gravity. They are related by the following equation:
g = GM/R^2
Where M is the mass of the earth and R is the radius of the earth.
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