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A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]
- a)total kinetic energy is conserved
- b)the angular momentum of the sphere about the point of contact with the plane is conserved
- c)only the rotational kinetic energy about the centre of mass is conserved
- d)an gular momen tum about the centre of mass is conserved.
Correct answer is option 'B'. Can you explain this answer?
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A solid homogeneous sphere of mass M and radius R is moving on a rough...
Angular momentum a bout the point of contact with the surface includes the angular momentum about the centre. Due to friction linear momentum is conserved.
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A solid homogeneous sphere of mass M and radius R is moving on a rough...
The correct answer is option 'B', which states that the angular momentum of the sphere about the point of contact with the plane is conserved. Let's understand why this is the correct answer in detail.
Conservation of Angular Momentum:
Angular momentum is a property of rotating objects and is defined as the product of the moment of inertia and the angular velocity. In the absence of any external torque, the total angular momentum of a system remains constant.
Rolling and Sliding Motion:
When a solid sphere is moving on a rough horizontal surface, it can have both rolling and sliding motion. Rolling motion occurs when the sphere rotates about its own axis while also translating along the surface. Sliding motion occurs when the sphere slides without any rotation.
Angular Momentum about the Point of Contact:
The point of contact between the sphere and the plane is fixed. The angular momentum of the sphere with respect to this point can be calculated using the formula:
L = Iω,
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Conservation of Angular Momentum:
In this scenario, the frictional force between the sphere and the surface exerts a torque on the sphere, causing it to both roll and slide. However, the net external torque acting on the sphere is zero, as no external torque is applied to the system.
According to the principle of conservation of angular momentum, when the net external torque is zero, the total angular momentum of the system remains constant.
Hence, the angular momentum of the sphere about the point of contact with the plane is conserved.
Explanation of Other Options:
- Option 'A': Total kinetic energy is not conserved because some of the kinetic energy is converted into other forms of energy, such as heat, due to the presence of friction.
- Option 'C': Rotational kinetic energy about the center of mass is not conserved because some of the rotational kinetic energy is converted into translational kinetic energy during rolling motion.
- Option 'D': Angular momentum about the center of mass is not conserved because there is an external torque acting on the sphere due to friction.
Conclusion:
In summary, during the motion of a solid sphere on a rough horizontal surface, the angular momentum of the sphere about the point of contact with the plane is conserved. This is because the net external torque acting on the sphere is zero. The conservation of angular momentum is a fundamental principle in physics and is applicable in various other scenarios as well.
Conservation of Angular Momentum:
Angular momentum is a property of rotating objects and is defined as the product of the moment of inertia and the angular velocity. In the absence of any external torque, the total angular momentum of a system remains constant.
Rolling and Sliding Motion:
When a solid sphere is moving on a rough horizontal surface, it can have both rolling and sliding motion. Rolling motion occurs when the sphere rotates about its own axis while also translating along the surface. Sliding motion occurs when the sphere slides without any rotation.
Angular Momentum about the Point of Contact:
The point of contact between the sphere and the plane is fixed. The angular momentum of the sphere with respect to this point can be calculated using the formula:
L = Iω,
where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Conservation of Angular Momentum:
In this scenario, the frictional force between the sphere and the surface exerts a torque on the sphere, causing it to both roll and slide. However, the net external torque acting on the sphere is zero, as no external torque is applied to the system.
According to the principle of conservation of angular momentum, when the net external torque is zero, the total angular momentum of the system remains constant.
Hence, the angular momentum of the sphere about the point of contact with the plane is conserved.
Explanation of Other Options:
- Option 'A': Total kinetic energy is not conserved because some of the kinetic energy is converted into other forms of energy, such as heat, due to the presence of friction.
- Option 'C': Rotational kinetic energy about the center of mass is not conserved because some of the rotational kinetic energy is converted into translational kinetic energy during rolling motion.
- Option 'D': Angular momentum about the center of mass is not conserved because there is an external torque acting on the sphere due to friction.
Conclusion:
In summary, during the motion of a solid sphere on a rough horizontal surface, the angular momentum of the sphere about the point of contact with the plane is conserved. This is because the net external torque acting on the sphere is zero. The conservation of angular momentum is a fundamental principle in physics and is applicable in various other scenarios as well.
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A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]a)total kinetic energy is conservedb)the angular momentum of the sphere about the point of contact with the plane is conservedc)only the rotational kinetic energy about the centre of mass is conservedd)an gular momen tum about the centre of mass is conserved.Correct answer is option 'B'. Can you explain this answer?
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A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]a)total kinetic energy is conservedb)the angular momentum of the sphere about the point of contact with the plane is conservedc)only the rotational kinetic energy about the centre of mass is conservedd)an gular momen tum about the centre of mass is conserved.Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]a)total kinetic energy is conservedb)the angular momentum of the sphere about the point of contact with the plane is conservedc)only the rotational kinetic energy about the centre of mass is conservedd)an gular momen tum about the centre of mass is conserved.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]a)total kinetic energy is conservedb)the angular momentum of the sphere about the point of contact with the plane is conservedc)only the rotational kinetic energy about the centre of mass is conservedd)an gular momen tum about the centre of mass is conserved.Correct answer is option 'B'. Can you explain this answer?.
A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]a)total kinetic energy is conservedb)the angular momentum of the sphere about the point of contact with the plane is conservedc)only the rotational kinetic energy about the centre of mass is conservedd)an gular momen tum about the centre of mass is conserved.Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]a)total kinetic energy is conservedb)the angular momentum of the sphere about the point of contact with the plane is conservedc)only the rotational kinetic energy about the centre of mass is conservedd)an gular momen tum about the centre of mass is conserved.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid homogeneous sphere of mass M and radius R is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere [1988]a)total kinetic energy is conservedb)the angular momentum of the sphere about the point of contact with the plane is conservedc)only the rotational kinetic energy about the centre of mass is conservedd)an gular momen tum about the centre of mass is conserved.Correct answer is option 'B'. Can you explain this answer?.
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