<–2/”>a >Newton’s law of universal Gravitation states that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Gravitation
Gravitation is the force by which every mass or particle of matter, including photons, attracts and is attracted by every other mass or particle of matter.The gravitational field at any point P in space is defined as the Gravitational Force felt by a tiny unit mass placed at P.
Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.
Mathematically, this law, and the magnitude of the force due to the gravitational interaction between two particles, is expressed with :-
Properties of Gravitational Force.
It is always attractive in nature while electric and magnetic force can be attractive or repulsive.
It is independent of the medium between the particles while electric and magnetic force depend on the nature of the medium between the particles.
It holds good over a wide range of distances. It is found true for interplanetary to inter atomic distances.
It is a central force i.e. acts along the line joining the centres of two interacting bodies.
It is a two-body interaction i.e. gravitational force between two particles is independent of the presence or absence of other particles.
It is the weakest force in nature : As Fnuclear > F electromagnetic > F gravitational .
It is a conservative force i.e. work done by it is path independent or work done in moving a particle round a closed path under the action of gravitational force is zero.
It is an action reaction pair i.e. the force with which one body (say earth) attracts the second body (say moon) is equal to the force with which moon attracts the earth.,
The Universal Law of Gravitation
The universal law of gravitation is a physical law that states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This law was first formulated by Isaac Newton in the late 17th century, and it has been one of the most important laws of physics ever since.
The universal law of gravitation can be expressed mathematically as follows:
$$F = G\frac{m_1m_2}{r^2}$$
where $F$ is the force of gravity, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.
The gravitational constant $G$ is a very small number, but it has a very important effect on the universe. The gravitational force between two objects is proportional to the product of their masses, so the more massive two objects are, the stronger the gravitational force between them. The gravitational force is also inversely proportional to the square of the distance between two objects, so the closer two objects are, the stronger the gravitational force between them.
The universal law of gravitation has many important applications in physics and astronomy. It can be used to calculate the orbits of planets and satellites, the trajectories of projectiles, and the tides. It can also be used to explain the formation of stars and galaxies.
Gravity
Gravity is a fundamental force of nature that causes all objects with mass or energy to be attracted to one another. It is the weakest of the four fundamental forces, but it is the most important force for large objects. Gravity is what keeps the Earth in orbit around the Sun and the Moon in orbit around the Earth. It is also what causes objects to fall to the ground when they are dropped.
The force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that the more massive two objects are, the stronger the gravitational force between them. The closer two objects are, the stronger the gravitational force between them.
The force of gravity is what causes objects to fall to the ground. When you drop an object, it accelerates towards the ground at a rate of 9.8 meters per second squared. This is called the acceleration due to gravity. The acceleration due to gravity is the same for all objects, regardless of their mass.
Gravity is a very important force in our lives. It is what keeps us on the ground and allows us to walk, run, and jump. It is also what causes the Earth to rotate on its axis and orbit the Sun. Without gravity, life as we know it would not be possible.
Acceleration Due to Gravity
Acceleration due to gravity is the rate at which an object accelerates due to the force of gravity. The acceleration due to gravity on Earth is 9.8 m/s^2. This means that an object in free fall will increase its speed by 9.8 m/s every second.
The acceleration due to gravity is not the same for all objects. It depends on the mass of the object and the mass of the planet or other object that is causing the gravitational force. For example, the acceleration due to gravity on the Moon is only 1.6 m/s^2. This is because the Moon has less mass than the Earth.
The acceleration due to gravity can be calculated using the following formula:
$$a = \frac{GM}{r^2}$$
where $a$ is the acceleration due to gravity, $G$ is the gravitational constant, $M$ is the mass of the planet or other object that is causing the gravitational force, and $r$ is the distance between the object and the center of the planet or other object.
The acceleration due to gravity is an important factor in many different fields, including physics, astronomy, and engineering. It is used to calculate the orbits of planets and satellites, the trajectories of projectiles, and the tides. It is also used to design structures that can withstand the force of gravity, such as buildings and bridges.
What is the force of gravity?
The force of gravity is a fundamental force of nature that attracts any two objects with mass. The more mass an object has, the stronger its gravitational pull.
What is the acceleration due to gravity?
The acceleration due to gravity is the rate at which an object accelerates due to the force of gravity. It is equal to 9.8 meters per second squared on Earth.
What is the difference between gravity and acceleration due to gravity?
Gravity is a force, while acceleration due to gravity is a rate of change of velocity. Gravity is what causes objects to fall to the ground, while acceleration due to gravity is what causes objects to accelerate towards the ground.
What is the law of universal gravitation?
The law of universal gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
What is the formula for the law of universal gravitation?
The formula for the law of universal gravitation is $F = G\frac{m_1m_2}{r^2}$, where $F$ is the force of gravity, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.
What is the value of the gravitational constant?
The value of the gravitational constant is $G = 6.67408 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2}$.
What is the gravitational field strength?
The gravitational field strength is the force of gravity per unit mass. It is equal to $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the object creating the gravitational field, and $r$ is the distance from the object.
What is the gravitational potential energy?
The gravitational potential energy is the energy that an object has due to its position in a gravitational field. It is equal to $U = -\frac{GMm}{r}$, where $G$ is the gravitational constant, $M$ is the mass of the object creating the gravitational field, $m$ is the mass of the object, and $r$ is the distance from the object.
What is the escape velocity?
The escape velocity is the minimum velocity an object must have to escape the gravitational pull of a planet or other object. It is equal to $v_e = \sqrt{\frac{2GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the object, and $r$ is the radius of the object.
What is the Roche limit?
The Roche limit is the distance from a planet or other object at which a satellite will break up due to tidal forces. It is equal to $r_R = 2.44 \frac{R_p}{3} \left(\frac{M_p}{M_s}\right)^{1/3}$, where $r_R$ is the Roche limit, $R_p$ is the radius of the planet, $M_p$ is the mass of the planet, and $M_s$ is the mass of the satellite.
What is the tidal force?
The tidal force is the difference in the gravitational force on two objects due to the difference in their distances from a third object. It is equal to $F_t = \frac{GMm}{r^3} \frac{d}{dr} \left(\frac{1}{r}\right)$, where $G$ is the gravitational constant, $M$ is the mass of the third object, $m$ is the mass of one of the two objects, $r$ is the distance between the third object and one of the two objects, and $d/dr \left(\frac{1}{r}\right)$ is the derivative of $1/r$ with respect to $r$.
What is the tidal bulge?
The tidal bulge is the deformation of an object due to the tidal force. It is equal to $\Delta h = \frac{3GM}{2r^3} \frac{d}{dr} \left(\frac{1}{r}\right)$, where $G$ is the gravitational constant, $M$ is the mass of the third object, $r$ is the distance between the third object and the object, and $d/dr \left(\frac{1}{r}\right
Sure, here are some MCQs about the topics of force, mass, and acceleration:
-
Which of the following is not a fundamental force?
(A) Gravity
(B) Electromagnetism
(C) The strong force
(D) The weak force -
Which of the following is the SI unit of force?
(A) Newton (N)
(B) Kilogram (kg)
(C) Meter (m)
(D) Second (s) -
Which of the following is the formula for the force of gravity between two objects?
(A) $F = G\frac{m_1m_2}{r^2}$
(B) $F = ma$
(C) $F = \frac{1}{2}mv^2$
(D) $F = \frac{k}{r^2}$ -
What is the acceleration due to gravity on Earth?
(A) 9.8 m/s^2
(B) 10 m/s^2
(C) 11 m/s^2
(D) 12 m/s^2 -
A 10-kg object is dropped from a height of 100 meters. What is its velocity when it hits the ground?
(A) 10 m/s
(B) 20 m/s
(C) 30 m/s
(D) 40 m/s -
A 20-kg object is thrown upwards with an initial velocity of 20 m/s. What is its velocity after 2 seconds?
(A) 10 m/s
(B) 20 m/s
(C) 30 m/s
(D) 40 m/s -
A 10-kg object is moving at a speed of 10 m/s. What is its kinetic energy?
(A) 50 J
(B) 100 J
(C) 150 J
(D) 200 J -
A 20-kg object is moving at a speed of 20 m/s. What is its momentum?
(A) 400 kg m/s
(B) 800 kg m/s
(C) 1200 kg m/s
(D) 1600 kg m/s -
A 10-kg object is moving at a speed of 10 m/s. What is its kinetic energy if it is moving in a circle of radius 1 meter?
(A) 50 J
(B) 100 J
(C) 150 J
(D) 200 J -
A 20-kg object is moving at a speed of 20 m/s. What is its momentum if it is moving in a circle of radius 1 meter?
(A) 400 kg m/s
(B) 800 kg m/s
(C) 1200 kg m/s
(D) 1600 kg m/s