Share & grow the world's knowledge!
We want to connect the people who have knowledge to the people who need it, to bring together people with different perspectives so they can understand each other better, and to empower everyone to share their knowledge.
If the gravitational force between two objects were proportional to 1/R (and not as 1/R²), where R is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed v, proportional to
If the gravitational force between two objects were proportional to 1/R instead of 1/R², the dynamics of objects in circular orbits would be very different. In such a case, the force acting on a particle in a circular orbit would decrease less rapidly with increasing distance R. This would change thRead more
If the gravitational force between two objects were proportional to 1/R instead of 1/R², the dynamics of objects in circular orbits would be very different. In such a case, the force acting on a particle in a circular orbit would decrease less rapidly with increasing distance R. This would change the dependence of the orbital speed of the particle on its distance from the center of attraction.
For an object in stable circular orbit, the necessary centripetal force for maintaining its orbit has to be supplied by the gravitational force. Gravitational force that depends on 1/R, the usual dependency of necessary orbital speed on R is broken. For this case, orbital speed in terms of given condition leads to a value of v not depending on R. This means that the orbital speed is independent of the distance from the center of attraction.
This behavior is in contrast to the 1/R² dependence of the actual gravitational force, where the orbital speed decreases with an increase in distance. The hypothetical 1/R force would result in strange orbital dynamics, as particles would have the same speed at all distances, which would fundamentally change the structure and stability of orbits in such a system.
See lessTwo particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed v of each particle is
When two particles of equal mass revolve about a common centre of mass under their mutual gravitational attraction, the balance between the gravitational force and the centripetal force for circular motion dictates their motion. Since masses are equal, the centre of mass lies at the midpoint on theRead more
When two particles of equal mass revolve about a common centre of mass under their mutual gravitational attraction, the balance between the gravitational force and the centripetal force for circular motion dictates their motion. Since masses are equal, the centre of mass lies at the midpoint on the line joining the two particles. Each particle revolves about the centre of mass in a circular path of radius R/2.
The gravitational force between the particles is what furnishes them with the required centripetal force. The gravitational force depends upon the masses of the particles and the distance separating them, which is given by R. On the other hand, centripetal force depends upon the mass of each particle, the orbital speed v, and the radius of their circular path.
From the equality of gravitational and centripetal forces, it follows that the orbital velocity of each particle is as follows: v = 1/2 √(Gm/R) It follows that speed of each particle is proportional to the square root of the constant of gravitation G and mass of the particle m and inversely proportional to the square root of R. The final expression for the speed is given by v = 1/2 √(Gm/R), which shows the relationship between mass, radius, and speed in this two-body system.
See lessTwo spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be
Gravitational force is one of the fundamental forces of nature that acts between two masses and depends only on the masses and the distance between them. It is governed by Newton's law of gravitation, which states that the gravitational force is proportional to the product of the two masses and inveRead more
Gravitational force is one of the fundamental forces of nature that acts between two masses and depends only on the masses and the distance between them. It is governed by Newton’s law of gravitation, which states that the gravitational force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centers.
When two spheres of masses m and M are kept in air, the gravitational force between them is F. It might appear that, if the space surrounding these masses be filled with a liquid of specific gravity 3, then the gravitational force might become affected. Gravitational force does not depend upon the medium surrounding the masses. It’s the universal force, independent on whether the masses are air, water, or even any other medium.
The specific gravity of the liquid affects only forces of a buoyant nature- that are independent of the actual gravitational attraction. As for buoyancy, it indeed determines an apparent weight, that’s different from the real gravitational attracting each other. Hence for such masses, where one’s space is filled with fluid with specific gravity 3, will not change the amount of gravitational force between it – it remains to be just F.
See lessHow do players execute the proper footwork while chasing in Kho-Kho?
Effective footwork is crucial for chasing in Kho-Kho. Players start with their left leg when moving left and the right leg for the right direction. Maintaining an upright posture and swinging arms naturally aids balance and speed. Proper footwork ensures that chasers can anticipate defenders' movemeRead more
Effective footwork is crucial for chasing in Kho-Kho. Players start with their left leg when moving left and the right leg for the right direction. Maintaining an upright posture and swinging arms naturally aids balance and speed. Proper footwork ensures that chasers can anticipate defenders’ movements, reducing the chances of missteps. This technique, combined with agility drills, enhances a chaser’s ability to close the gap quickly, improving overall gameplay and success in tagging defenders.
See lessWhat is the role of the defender in the game of Kho-Kho?
Defenders in Kho-Kho play a crucial role in challenging chasers by evading their attempts to tag. They use strategies like leaning, quick turns, and unpredictable movements to mislead chasers. The defender’s primary goal is to remain untagged for as long as possible, helping their team accumulate poRead more
Defenders in Kho-Kho play a crucial role in challenging chasers by evading their attempts to tag. They use strategies like leaning, quick turns, and unpredictable movements to mislead chasers. The defender’s primary goal is to remain untagged for as long as possible, helping their team accumulate points. Effective defending requires agility, anticipation, and smart decision-making, making defenders an integral part of the game’s strategy and excitement.
See less