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Show that gravitational field intensity at any point is equal to the free acceleration of a test mass placed at that point.
The intensity of the gravitational field at any point in space is proportional to the free acceleration felt by a test mass placed at that point. A small mass, which can be referred to as a test mass, will experience a gravitational force resulting from a more significant mass, for instance a planetRead more
The intensity of the gravitational field at any point in space is proportional to the free acceleration felt by a test mass placed at that point. A small mass, which can be referred to as a test mass, will experience a gravitational force resulting from a more significant mass, for instance a planet or star, whenever it is placed inside the gravitational field. This force causes test mass to accelerate toward the source of the gravitational field.
The gravitational field intensity, or force per unit mass, on an object at a point describes how intense the gravitational influence is in the direction at that point. The acceleration with which the test mass falls when released under gravity depends upon the massive body, falling towards it. This test mass acceleration reflects the strength and direction of the gravitational field intensity at that point.
Thus, there is an obvious relationship between gravitational field intensity and the acceleration of a test mass: the former represents the acceleration that any mass would undergo if placed in the gravitational field. In other words, gravitational field intensity measures the acceleration due to gravity at every point and proves that the two are intimately related. This concept is the foundation of several physics concepts such as motion under gravity and how objects move in gravitational fields.
See lessShow that the gravitational field intensity of the earth at any point is equal to the acceleration produced in the freely falling body at that point
The force experience due to gravitational pull, experienced by unit mass is considered as gravitational intensity field on any point located over Earth. Any object experiencing fall freely due to attraction, or force due to the action of gravity causes this falling, while the body attains a velocityRead more
The force experience due to gravitational pull, experienced by unit mass is considered as gravitational intensity field on any point located over Earth. Any object experiencing fall freely due to attraction, or force due to the action of gravity causes this falling, while the body attains a velocity along any desired trajectory. It tends toward center of the earth through its own acceleration, with gravitational pull due to earth acting over it.
When an object is dropped from rest and allowed to fall freely, it accelerates toward the Earth at a rate constant near the surface. The rate is determined by the mass of the Earth and the distance from its center. The gravitational field intensity at that point can be thought of as the gravitational force exerted on the object divided by its mass. Since the force causing the acceleration is the weight of the object, the gravitational field intensity directly relates to how quickly the object accelerates as it falls.
The intensity of gravitational field at any point in Earth is given by acceleration experienced by any freely falling body. In this context, it proves that this strength of gravitational field is indeed what causes an object to fall with acceleration so as to bring out the relation between intensity of gravitational field and the motion of falling bodies directly.
See lessWhat is meany by gravitational potential energy of a body? What is the zero level of potential energy?
Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. It is the amount of work done against the gravitational force in moving an object to a certain height above a reference point. This energy depends on the mass of the object, the height at wRead more
Gravitational potential energy is the energy possessed by a body due to its position in a gravitational field. It is the amount of work done against the gravitational force in moving an object to a certain height above a reference point. This energy depends on the mass of the object, the height at which it is located, and the strength of the gravitational field acting upon it. For instance, when an object is taken to a greater height, it is endowed with gravitational potential energy that can easily be changed into kinetic energy should the object fall.
Gravitational potential energy also relates to setting up a “zero level” of potential energy. A zero level of potential energy is established arbitrarily; most often, at ground level or infinity. When the zero level is set to be at ground level, the gravitational potential energy of an object at that height is zero. The gravitational potential energy will increase as the object moves above this level. In the case where the zero level is set at infinity, the potential energy of an object will approach zero as it moves infinitely far away from any massive body. This zero level provides for uniform calculations of potential energy in different settings and makes the analysis of gravitational interactions easier.
See lessDerive an expression for the gravitational potential energy of a body of m located at distance r from the centre of the earth.
To derive the expression for the gravitational potential energy of a body with mass m located at a distance r from the center of the Earth, we begin by understanding that gravitational potential energy is the energy associated with the position of an object in a gravitational field. When an object iRead more
To derive the expression for the gravitational potential energy of a body with mass m located at a distance r from the center of the Earth, we begin by understanding that gravitational potential energy is the energy associated with the position of an object in a gravitational field.
When an object is at a distance r from the center of the Earth, it feels a gravitational force due to the mass of the Earth. To determine the gravitational potential energy we consider the work done against this gravitational force in moving an object from a reference point, which is often considered to be infinity, at which the potential energy is zero, to the distance r.
The gravitational force acting on the mass is given by Newton’s law of gravitation as is proportional to the product of the masses and inversely proportional to the square of the distance between them. In order to obtain the expression for potential energy, it is necessary to integrate that force over the distance from infinity to. This results in an expression for gravitational potential energy that tells the amount of energy stored for being at a certain location within the gravitational field.
See lessA Black hole is a body from whose surface nothing may evan escape. What is the condition for an uniform spherical body of amss M to be a black hole? What should be the radius of such a black hole if its mass is nine times the mass of the earth?
A black hole is a collapsed massive body under its own gravity to a point where its escape velocity exceeds the speed of light. For an object to be a black hole, it must satisfy the condition known as the Schwarzschild radius, which defines the size of the event horizon-the boundary beyond which notRead more
A black hole is a collapsed massive body under its own gravity to a point where its escape velocity exceeds the speed of light. For an object to be a black hole, it must satisfy the condition known as the Schwarzschild radius, which defines the size of the event horizon-the boundary beyond which nothing can escape.
The condition for a uniform spherical body of mass M to be a black hole is that the radius must be less than or equal to the Schwarzschild radius. Now, the Schwarzschild radius, or rₛ, is directly proportional to the mass of the body and can be easily expressed in terms of its mass. A body, when its radius is equal to its Schwarzschild radius, is a black hole.
If we take a black hole of mass nine times the Earth’s mass, we can calculate its Schwarzschild radius. Earth’s mass is about 5.97 x 10²⁴ kilograms. Therefore, the mass of the black hole would be 9 x 5.97 x 10²⁴ kg. Using the formula for the Schwarzschild radius, we can calculate the particular radius for this black hole. This radius will set the point at which the speed of escape equals the speed of light and thus form a black hole.
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