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What is concept of mutual gravitational attraction in center of mass?
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What is concept of mutual gravitational attraction in center of mass?
Understanding Mutual Gravitational Attraction in the Center of Mass

Understanding the Concept:
- The mutual gravitational attraction between two objects is the force of attraction that exists between them due to their masses.
- This force is always directed along the line that connects the centers of mass of the two objects.

Center of Mass:
- The center of mass is the point where the entire mass of an object can be considered to be concentrated.
- In a system of two objects, the center of mass is the point where the gravitational forces between the two objects can be considered to act.

Mutual Gravitational Attraction:
- The mutual gravitational attraction between two objects in the center of mass can be understood using Newton's law of universal gravitation.
- According to this law, the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass.
- This force can be calculated using the formula F = G * (m1 * m2) / r^2, where F is the force of attraction, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers of mass.

Importance:
- Understanding mutual gravitational attraction in the center of mass is crucial in various fields such as astronomy, physics, and engineering.
- It helps in predicting the motion of celestial bodies, designing spacecraft trajectories, and analyzing the stability of structures.

In conclusion, the concept of mutual gravitational attraction in the center of mass is fundamental to understanding the interactions between objects in the universe. By considering the center of mass and applying the laws of gravitation, scientists and engineers can make accurate predictions and calculations in a wide range of applications.
Community Answer
What is concept of mutual gravitational attraction in center of mass?
As per my knowledge,
each pair of masses attract each other with equal forces along the imaginary line joining their center of mass. So while solving question we can directly apply the forces on the respective center of mass.
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Position of centre of massIn a uniform gravitational field the centre of mass coincide with the centre of gravity. But these two points do not always coincide, however. For example, the Moon’s centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform spher e), but its centre of gravity is slightly displaced towards Earth because of the stronger gravitational force on the Moon’s near side facing the earth. If an object does not have a uniform weight distribution then the center of mass will be closer to where most of the weight is located. For example, the center of gravity for a hammer is located close to where the head connects to the handle. The center of mass can be located at an empty point in space, such as the center of a hollow ball. The center of gravity can even be completely outside of an object, such as for a donut or a curved banana.Standing upright, an adult human’s centre of mass is located roughly at the center of their torso. The centre of mass rises a few inches when with rising arms.The center of gravity can even be at a point outside the body, such as when bent over in an inverted-U pose.An object is in balanced position if its center of gravity is above its base of support. For the two cylinders below, the left cylinder’s CG is above the base of support so the upward support force from the base is aligned with the downward force of gravity. For the cylinder on the right the CG is not above the base of support so these two forces cannot align and instead create a torque that rotates the object, tipping it over.Does the centre of mass does not coincide with the centre of gravity of a body?

Position of centre of massIn a uniform gravitational field the centre of mass coincide with the centre of gravity. But these two points do not always coincide, however. For example, the Moon’s centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform spher e), but its centre of gravity is slightly displaced towards Earth because of the stronger gravitational force on the Moon’s near side facing the earth. If an object does not have a uniform weight distribution then the center of mass will be closer to where most of the weight is located. For example, the center of gravity for a hammer is located close to where the head connects to the handle. The center of mass can be located at an empty point in space, such as the center of a hollow ball. The center of gravity can even be completely outside of an object, such as for a donut or a curved banana.Standing upright, an adult human’s centre of mass is located roughly at the center of their torso. The centre of mass rises a few inches when with rising arms.The center of gravity can even be at a point outside the body, such as when bent over in an inverted-U pose.An object is in balanced position if its center of gravity is above its base of support. For the two cylinders below, the left cylinder’s CG is above the base of support so the upward support force from the base is aligned with the downward force of gravity. For the cylinder on the right the CG is not above the base of support so these two forces cannot align and instead create a torque that rotates the object, tipping it over.The leaning tower of Pisa does not fall since

Position of centre of massIn a uniform gravitational field the centre of mass coincide with the centre of gravity. But these two points do not always coincide, however. For example, the Moon’s centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform spher e), but its centre of gravity is slightly displaced towards Earth because of the stronger gravitational force on the Moon’s near side facing the earth. If an object does not have a uniform weight distribution then the center of mass will be closer to where most of the weight is located. For example, the center of gravity for a hammer is located close to where the head connects to the handle. The center of mass can be located at an empty point in space, such as the center of a hollow ball. The center of gravity can even be completely outside of an object, such as for a donut or a curved banana.Standing upright, an adult human’s centre of mass is located roughly at the center of their torso. The centre of mass rises a few inches when with rising arms.The center of gravity can even be at a point outside the body, such as when bent over in an inverted-U pose.An object is in balanced position if its center of gravity is above its base of support. For the two cylinders below, the left cylinder’s CG is above the base of support so the upward support force from the base is aligned with the downward force of gravity. For the cylinder on the right the CG is not above the base of support so these two forces cannot align and instead create a torque that rotates the object, tipping it over.Two similar blocks are shown below. The first block is top-heavy and the second block is bottom heavy. Where the centers of mass will be located?

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