The position vector of a center of mass in an n-particle system can be determined by a weighted average of the positions of the particles, and their masses play roles as weights. This average is influenced by the total mass in the system. According to Newton's second law, the motion of the center ofRead more
The position vector of a center of mass in an n-particle system can be determined by a weighted average of the positions of the particles, and their masses play roles as weights. This average is influenced by the total mass in the system. According to Newton’s second law, the motion of the center of mass is given by the fact that the total external force acting on the system is equal to the mass of the system multiplied by the acceleration of the center of mass. The acceleration of the center of mass is also determined by the net external forces acting on each individual particle so that it can behave like a single point mass.
The location of the center of mass in a two-particle system is determined by a weighted average of the positions of the two particles, with their masses serving as weights. This means that the center of mass is influenced more by the particle with the larger mass. If the particles have equal mass, tRead more
The location of the center of mass in a two-particle system is determined by a weighted average of the positions of the two particles, with their masses serving as weights. This means that the center of mass is influenced more by the particle with the larger mass. If the particles have equal mass, the center of mass will lie halfway between them. Conversely, if one mass is significantly larger, then the center will be closer to it. For the purposes of computation, the center of mass may be treated as a point with the entire mass concentrated there, which affects the motion and stability of a system in many applications.
The weight of an object on the Moon is approximately one-sixth that of its weight on Earth. This is because the Moon has less gravitational force since it has a smaller mass and size. Thus, any object that weighs more on Earth will weigh much less when measured on the Moon. For example, an object thRead more
The weight of an object on the Moon is approximately one-sixth that of its weight on Earth. This is because the Moon has less gravitational force since it has a smaller mass and size. Thus, any object that weighs more on Earth will weigh much less when measured on the Moon. For example, an object that weighs 60 kilograms on Earth would weigh approximately 10 kilograms on the Moon. This difference in weight is an example of how the gravitational pull varies between celestial bodies and how objects behave in different environments throughout the solar system.
Tides on Earth are mainly caused by the gravitational pull of the Moon. As the Moon orbits the Earth, its gravitational force creates bulges in the oceans, resulting in high tides in those regions. Although the Sun also exerts a gravitational pull that affects tides, its influence is significantly lRead more
Tides on Earth are mainly caused by the gravitational pull of the Moon. As the Moon orbits the Earth, its gravitational force creates bulges in the oceans, resulting in high tides in those regions. Although the Sun also exerts a gravitational pull that affects tides, its influence is significantly less than that of the Moon. The Earth’s rotation contributes to the timing and frequency of tides, but tidal movements are primarily due to the gravitational interaction with the Moon. Even though ocean currents do not create tides, they may contribute to patterns or behavior of the tidal waters at the coastal shores.
Jupiter is the strongest in terms of gravitational pull compared to all other planets in the solar system. It is so large and has such a massive mass that its gravity affects the orbits of other nearby celestial bodies, including moons and asteroids. Its gravitational strength also helps protect theRead more
Jupiter is the strongest in terms of gravitational pull compared to all other planets in the solar system. It is so large and has such a massive mass that its gravity affects the orbits of other nearby celestial bodies, including moons and asteroids. Its gravitational strength also helps protect the inner planets from some potential asteroid impacts by pulling them into its orbit. While Earth, Mars, and Saturn also have notable gravitational forces, none compare to Jupiter’s. Its dominant gravity plays a key role in the dynamics of the solar system, making it an essential factor in maintaining its overall structure and balance.
Geostationary satellites mainly find application in communication because it is stationary from a particular spot on Earth. Such a static position makes the satellite suitable for the transmission of television signals and internet services along with long distance communication. Orbits are fixed toRead more
Geostationary satellites mainly find application in communication because it is stationary from a particular spot on Earth. Such a static position makes the satellite suitable for the transmission of television signals and internet services along with long distance communication. Orbits are fixed to place them so that continuously the same place is covered for unbroken lines of communication. While geostationary satellites are used for weather forecasting and, to a lesser extent, navigation, the core role of geostationary satellites is for communication. They are not mainly used for space exploratory purposes due to their fixed position and function, which are optimized for Earth-based applications in lieu of interplanetary or deep-space missions.
The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one's location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the coRead more
The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one’s location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the core, at elevated heights, because the distance from the earth’s center now increases, gravitation diminishes. In both scenarios, the acceleration due to gravity is reduced since it is proportional to the mass and distance of the body involved. Such differences are essential for determining gravitational changes across different regions on Earth or within the surrounding space.
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses servinRead more
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses serving as weights. The position of the center of mass lies closer to the particle with the larger mass. If the masses are equal, the centre of mass is exactly between the two particles. The above concept applies universally to any two-particle system, regardless of the values of distances or mass.
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is aRead more
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is a weighted average of the individual particle velocities.
According to Newton’s second law, the change in momentum of the system is equal to the net external force. In the absence of external forces, the total momentum remains constant, implying that the velocity of the center of mass also remains constant.
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to theRead more
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to the heavier region. The shape of the body is also involved in this; symmetrical shapes have their center of mass at the center of symmetry, while asymmetrical shapes have it offset from that point. Disturbance in density would further shift the positions of the center of mass toward denser regions. For systems of bodies, further external forces or constraints can affect its position.
Write an expression for the position vector of the centre of mass of n-particle system. Also write the equations of motion which govern the motion of the centre of mass.
The position vector of a center of mass in an n-particle system can be determined by a weighted average of the positions of the particles, and their masses play roles as weights. This average is influenced by the total mass in the system. According to Newton's second law, the motion of the center ofRead more
The position vector of a center of mass in an n-particle system can be determined by a weighted average of the positions of the particles, and their masses play roles as weights. This average is influenced by the total mass in the system. According to Newton’s second law, the motion of the center of mass is given by the fact that the total external force acting on the system is equal to the mass of the system multiplied by the acceleration of the center of mass. The acceleration of the center of mass is also determined by the net external forces acting on each individual particle so that it can behave like a single point mass.
See lessWrite an expression for the location of centre of mass of a two particle system. Discuss the result.
The location of the center of mass in a two-particle system is determined by a weighted average of the positions of the two particles, with their masses serving as weights. This means that the center of mass is influenced more by the particle with the larger mass. If the particles have equal mass, tRead more
The location of the center of mass in a two-particle system is determined by a weighted average of the positions of the two particles, with their masses serving as weights. This means that the center of mass is influenced more by the particle with the larger mass. If the particles have equal mass, the center of mass will lie halfway between them. Conversely, if one mass is significantly larger, then the center will be closer to it. For the purposes of computation, the center of mass may be treated as a point with the entire mass concentrated there, which affects the motion and stability of a system in many applications.
See lessThe weight of an object on the Moon is:
The weight of an object on the Moon is approximately one-sixth that of its weight on Earth. This is because the Moon has less gravitational force since it has a smaller mass and size. Thus, any object that weighs more on Earth will weigh much less when measured on the Moon. For example, an object thRead more
The weight of an object on the Moon is approximately one-sixth that of its weight on Earth. This is because the Moon has less gravitational force since it has a smaller mass and size. Thus, any object that weighs more on Earth will weigh much less when measured on the Moon. For example, an object that weighs 60 kilograms on Earth would weigh approximately 10 kilograms on the Moon. This difference in weight is an example of how the gravitational pull varies between celestial bodies and how objects behave in different environments throughout the solar system.
See lessTides on Earth are caused primarily by:
Tides on Earth are mainly caused by the gravitational pull of the Moon. As the Moon orbits the Earth, its gravitational force creates bulges in the oceans, resulting in high tides in those regions. Although the Sun also exerts a gravitational pull that affects tides, its influence is significantly lRead more
Tides on Earth are mainly caused by the gravitational pull of the Moon. As the Moon orbits the Earth, its gravitational force creates bulges in the oceans, resulting in high tides in those regions. Although the Sun also exerts a gravitational pull that affects tides, its influence is significantly less than that of the Moon. The Earth’s rotation contributes to the timing and frequency of tides, but tidal movements are primarily due to the gravitational interaction with the Moon. Even though ocean currents do not create tides, they may contribute to patterns or behavior of the tidal waters at the coastal shores.
See lessThe planet with the strongest gravitational pull in our solar system is:

Jupiter is the strongest in terms of gravitational pull compared to all other planets in the solar system. It is so large and has such a massive mass that its gravity affects the orbits of other nearby celestial bodies, including moons and asteroids. Its gravitational strength also helps protect theRead more
Jupiter is the strongest in terms of gravitational pull compared to all other planets in the solar system. It is so large and has such a massive mass that its gravity affects the orbits of other nearby celestial bodies, including moons and asteroids. Its gravitational strength also helps protect the inner planets from some potential asteroid impacts by pulling them into its orbit. While Earth, Mars, and Saturn also have notable gravitational forces, none compare to Jupiter’s. Its dominant gravity plays a key role in the dynamics of the solar system, making it an essential factor in maintaining its overall structure and balance.
See lessGeostationary satellites are primarily used for:
Geostationary satellites mainly find application in communication because it is stationary from a particular spot on Earth. Such a static position makes the satellite suitable for the transmission of television signals and internet services along with long distance communication. Orbits are fixed toRead more
Geostationary satellites mainly find application in communication because it is stationary from a particular spot on Earth. Such a static position makes the satellite suitable for the transmission of television signals and internet services along with long distance communication. Orbits are fixed to place them so that continuously the same place is covered for unbroken lines of communication. While geostationary satellites are used for weather forecasting and, to a lesser extent, navigation, the core role of geostationary satellites is for communication. They are not mainly used for space exploratory purposes due to their fixed position and function, which are optimized for Earth-based applications in lieu of interplanetary or deep-space missions.
See lessThe acceleration due to gravity decreases with:
The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one's location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the coRead more
The acceleration due to gravity diminishes with increasing depth and height relative to the surface of the Earth. Moving toward the Earth core, only the mass beneath one’s location participates in producing gravity, reducing what is often known as the local gravity. Similar to moving out from the core, at elevated heights, because the distance from the earth’s center now increases, gravitation diminishes. In both scenarios, the acceleration due to gravity is reduced since it is proportional to the mass and distance of the body involved. Such differences are essential for determining gravitational changes across different regions on Earth or within the surrounding space.
See lessDerive an expression for the centre of mass of a two particle system from ab-inito.
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses servinRead more
To find the center of mass of a two-particle system, consider two particles with specific masses and positions. The center of mass is that point where the total mass of the system effectively acts. It is determined as a weighted average of the positions of the two particles, with their masses serving as weights. The position of the center of mass lies closer to the particle with the larger mass. If the masses are equal, the centre of mass is exactly between the two particles. The above concept applies universally to any two-particle system, regardless of the values of distances or mass.
See lessShow that in the absence of any external force, the velocity of the centre of mass remains constant.
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is aRead more
To show that the velocity of the center of mass is constant when there are no external forces, we start with the definition of the center of mass in terms of masses and positions of particles in a system. By taking the derivative of this position, we see that the velocity of the center of mass is a weighted average of the individual particle velocities.
See lessAccording to Newton’s second law, the change in momentum of the system is equal to the net external force. In the absence of external forces, the total momentum remains constant, implying that the velocity of the center of mass also remains constant.
State the factors on which the position of the centre of mass of a rigid body depends.
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to theRead more
The position of the center of mass in the rigid body depends on several factors. One of these includes the distribution of mass within the object. Thus, an object of uniformly distributed mass has a center of mass at its geometric center, while an unevenly distributed mass has a center nearer to the heavier region. The shape of the body is also involved in this; symmetrical shapes have their center of mass at the center of symmetry, while asymmetrical shapes have it offset from that point. Disturbance in density would further shift the positions of the center of mass toward denser regions. For systems of bodies, further external forces or constraints can affect its position.
See less