When a solid sphere is put on a smooth horizontal plane and a horizontal force is applied, the position where the force has been applied varies with the motion of the ball. The applied force can make both linear motion of the centre of mass and rotational motion about the center. As the result of thRead more
When a solid sphere is put on a smooth horizontal plane and a horizontal force is applied, the position where the force has been applied varies with the motion of the ball. The applied force can make both linear motion of the centre of mass and rotational motion about the center.
As the result of this, the effect of rotation will depend upon the height at which the force has been applied. If the force is applied above the center of the sphere, it creates torque and causes rotation. This decreases the fraction of the force that can be used to accelerate the center of mass linearly. On the other hand, if the force is applied lower on the sphere, closer to its base, the torque is smaller, and a greater fraction of the applied force contributes to linear acceleration.
The linear acceleration of the sphere can be maximized only when the torque is at its minimum. This occurs when the force is applied at the lowest point of the sphere. In this case, the force passes directly through the center of mass of the sphere, meaning there is no rotation and all of the force applied will be utilized for linear acceleration.
Therefore, the maximum acceleration of the center of mass of the sphere occurs when the horizontal force is applied at the lowest point on the sphere.
The center of mass of a system of particles is the average position of all the particles, weighted by their masses. It is an intrinsic property of the system and depends on the positions and masses of the individual particles. The position of the center of mass is calculated based on the distributioRead more
The center of mass of a system of particles is the average position of all the particles, weighted by their masses. It is an intrinsic property of the system and depends on the positions and masses of the individual particles. The position of the center of mass is calculated based on the distribution of mass within the system and the relative distances between the particles.
However, it must be stressed that these forces don’t cause an effect in determining the place of the center of mass at a given instant of time. As for a change in position with time for a given overall force acting upon the system, changing positions with external influences, its intrinsic position as for the configuration does not. For example, if a system of particles is exposed to gravity or an external push, then the center moves relative to the center of mass according to the net force. However, its position relative to the system remains unchanged.
The center of mass is determined purely by the spatial arrangement and masses of the particles, independent of any forces on the system, making it a very basic concept in explaining the motion and behavior of physical systems.
The acceleration due to gravity is directly proportional to the density of a planet, assuming the radius remains constant. This means that if the density of a planet doubles, the value of gravity on its surface also doubles. For example, increasing a planet's density while maintaining the same sizeRead more
The acceleration due to gravity is directly proportional to the density of a planet, assuming the radius remains constant. This means that if the density of a planet doubles, the value of gravity on its surface also doubles. For example, increasing a planet’s density while maintaining the same size results in a stronger gravitational pull.
This relationship highlights how changes in a planet’s internal composition, such as an increase in mass per unit volume, can significantly impact its gravitational force. Thus, doubling the density leads to a direct doubling of the gravitational acceleration experienced on the planet’s surface.
g = 4/3πGRp i.e, g ∝ p
If density is doubled, then the value of g also gets doubled.
The acceleration due to gravity for a body on the Earth’s surface depends on the mass of the Earth and its radius. It is directly proportional to the Earth's mass and inversely proportional to the square of its radius. This means that as the mass of the Earth increases, the gravitational pull also iRead more
The acceleration due to gravity for a body on the Earth’s surface depends on the mass of the Earth and its radius. It is directly proportional to the Earth’s mass and inversely proportional to the square of its radius. This means that as the mass of the Earth increases, the gravitational pull also increases, making the acceleration due to gravity stronger.
Conversely, if the radius of the Earth increases while keeping its mass constant, the gravitational force weakens, reducing the acceleration due to gravity. This proportional relationship explains how Earth’s mass and size influence gravity experienced at its surface.
The gravitational force between two objects is influenced by their masses, the distance between them, and the density of the material involved. When the mass of an object is expressed in terms of its volume and density, the force becomes proportional to the fourth power of the radius, assuming the dRead more
The gravitational force between two objects is influenced by their masses, the distance between them, and the density of the material involved. When the mass of an object is expressed in terms of its volume and density, the force becomes proportional to the fourth power of the radius, assuming the density remains constant.
This relationship indicates that as the radius of an object increases, the gravitational force grows significantly due to the radius being raised to the fourth power. This dependence on radius highlights the impact of size and density in determining the strength of gravitational interactions.
F = G (m x m)/((2 R)²) = G ((4/3 πR³p)²)/(4 R²)
F ∝ R⁴
A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct?
When a solid sphere is put on a smooth horizontal plane and a horizontal force is applied, the position where the force has been applied varies with the motion of the ball. The applied force can make both linear motion of the centre of mass and rotational motion about the center. As the result of thRead more
When a solid sphere is put on a smooth horizontal plane and a horizontal force is applied, the position where the force has been applied varies with the motion of the ball. The applied force can make both linear motion of the centre of mass and rotational motion about the center.
As the result of this, the effect of rotation will depend upon the height at which the force has been applied. If the force is applied above the center of the sphere, it creates torque and causes rotation. This decreases the fraction of the force that can be used to accelerate the center of mass linearly. On the other hand, if the force is applied lower on the sphere, closer to its base, the torque is smaller, and a greater fraction of the applied force contributes to linear acceleration.
The linear acceleration of the sphere can be maximized only when the torque is at its minimum. This occurs when the force is applied at the lowest point of the sphere. In this case, the force passes directly through the center of mass of the sphere, meaning there is no rotation and all of the force applied will be utilized for linear acceleration.
Therefore, the maximum acceleration of the center of mass of the sphere occurs when the horizontal force is applied at the lowest point on the sphere.
Checkout for more information: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessThe centre of mass of a system of particles does not depend on
The center of mass of a system of particles is the average position of all the particles, weighted by their masses. It is an intrinsic property of the system and depends on the positions and masses of the individual particles. The position of the center of mass is calculated based on the distributioRead more
The center of mass of a system of particles is the average position of all the particles, weighted by their masses. It is an intrinsic property of the system and depends on the positions and masses of the individual particles. The position of the center of mass is calculated based on the distribution of mass within the system and the relative distances between the particles.
However, it must be stressed that these forces don’t cause an effect in determining the place of the center of mass at a given instant of time. As for a change in position with time for a given overall force acting upon the system, changing positions with external influences, its intrinsic position as for the configuration does not. For example, if a system of particles is exposed to gravity or an external push, then the center moves relative to the center of mass according to the net force. However, its position relative to the system remains unchanged.
The center of mass is determined purely by the spatial arrangement and masses of the particles, independent of any forces on the system, making it a very basic concept in explaining the motion and behavior of physical systems.
Click here : – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
See lessIf the density of earth is doubled keeping its radius constant, then acceleration due to gravity g is
The acceleration due to gravity is directly proportional to the density of a planet, assuming the radius remains constant. This means that if the density of a planet doubles, the value of gravity on its surface also doubles. For example, increasing a planet's density while maintaining the same sizeRead more
The acceleration due to gravity is directly proportional to the density of a planet, assuming the radius remains constant. This means that if the density of a planet doubles, the value of gravity on its surface also doubles. For example, increasing a planet’s density while maintaining the same size results in a stronger gravitational pull.
This relationship highlights how changes in a planet’s internal composition, such as an increase in mass per unit volume, can significantly impact its gravitational force. Thus, doubling the density leads to a direct doubling of the gravitational acceleration experienced on the planet’s surface.
g = 4/3πGRp i.e, g ∝ p
See lessIf density is doubled, then the value of g also gets doubled.
Acceleration due to gravity g for a body of mass m on earth’s surface is proportional (Radius of earth = R, mass of earth = M) to)
The acceleration due to gravity for a body on the Earth’s surface depends on the mass of the Earth and its radius. It is directly proportional to the Earth's mass and inversely proportional to the square of its radius. This means that as the mass of the Earth increases, the gravitational pull also iRead more
The acceleration due to gravity for a body on the Earth’s surface depends on the mass of the Earth and its radius. It is directly proportional to the Earth’s mass and inversely proportional to the square of its radius. This means that as the mass of the Earth increases, the gravitational pull also increases, making the acceleration due to gravity stronger.
Conversely, if the radius of the Earth increases while keeping its mass constant, the gravitational force weakens, reducing the acceleration due to gravity. This proportional relationship explains how Earth’s mass and size influence gravity experienced at its surface.
g = GM/R² ∴ g ∝ M/R²
See lessTwo balls, each of radius R, equal mass and density are placed in contact, then the force of gravitation between them is proportional to
The gravitational force between two objects is influenced by their masses, the distance between them, and the density of the material involved. When the mass of an object is expressed in terms of its volume and density, the force becomes proportional to the fourth power of the radius, assuming the dRead more
The gravitational force between two objects is influenced by their masses, the distance between them, and the density of the material involved. When the mass of an object is expressed in terms of its volume and density, the force becomes proportional to the fourth power of the radius, assuming the density remains constant.
This relationship indicates that as the radius of an object increases, the gravitational force grows significantly due to the radius being raised to the fourth power. This dependence on radius highlights the impact of size and density in determining the strength of gravitational interactions.
F = G (m x m)/((2 R)²) = G ((4/3 πR³p)²)/(4 R²)
See lessF ∝ R⁴