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A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the sphere
- a)total kinetic energy is conserved
- b)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)angular momentum about centre of mass is conversed
Correct answer is option 'B'. Can you explain this answer?
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A solid homogeneous sphere is moving on a rough horizontal surface, p...
Angular momentum about point of contact is conserved because torque due to friction about point of contact will be zero.
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A solid homogeneous sphere is moving on a rough horizontal surface, p...
Explanation:
When a solid homogeneous sphere is moving on a rough horizontal surface, it experiences both rolling and sliding motion. Let's analyze the options given one by one to understand which one is correct.
a) Total kinetic energy is conserved:
In this case, the sphere is experiencing both rolling and sliding motion. Since kinetic energy is the sum of translational and rotational kinetic energies, and both translational and rotational energies are changing during the motion, the total kinetic energy is not conserved. Therefore, option 'a' is incorrect.
b) Angular momentum of the sphere about the point of contact with the plane is conserved:
When the sphere is rolling and sliding, the point of contact with the plane is stationary. The angular momentum of an object about a point is given by the product of the moment of inertia and angular velocity about that point. Since the point of contact is stationary, the angular velocity about that point is zero. Therefore, the angular momentum about the point of contact is also zero, and it remains constant throughout the motion. Hence, option 'b' is correct.
c) Only the rotational kinetic energy about the center of mass is conserved:
During the motion of the sphere, both the translational and rotational kinetic energies are changing. The rotational kinetic energy depends on the moment of inertia and the square of the angular velocity. Since the sphere is experiencing rolling and sliding, the angular velocity is not constant, and therefore, the rotational kinetic energy is not conserved. Hence, option 'c' is incorrect.
d) Angular momentum about the center of mass is conserved:
The angular momentum about the center of mass is given by the product of the moment of inertia about the center of mass and the angular velocity about the center of mass. As the sphere is experiencing both rolling and sliding motion, the angular velocity about the center of mass is changing. Therefore, the angular momentum about the center of mass is also changing and not conserved. Thus, option 'd' is incorrect.
Conclusion:
From the above analysis, we can conclude that the angular momentum of the sphere about the point of contact with the plane is conserved during the motion. Hence, option 'b' is the correct answer.
When a solid homogeneous sphere is moving on a rough horizontal surface, it experiences both rolling and sliding motion. Let's analyze the options given one by one to understand which one is correct.
a) Total kinetic energy is conserved:
In this case, the sphere is experiencing both rolling and sliding motion. Since kinetic energy is the sum of translational and rotational kinetic energies, and both translational and rotational energies are changing during the motion, the total kinetic energy is not conserved. Therefore, option 'a' is incorrect.
b) Angular momentum of the sphere about the point of contact with the plane is conserved:
When the sphere is rolling and sliding, the point of contact with the plane is stationary. The angular momentum of an object about a point is given by the product of the moment of inertia and angular velocity about that point. Since the point of contact is stationary, the angular velocity about that point is zero. Therefore, the angular momentum about the point of contact is also zero, and it remains constant throughout the motion. Hence, option 'b' is correct.
c) Only the rotational kinetic energy about the center of mass is conserved:
During the motion of the sphere, both the translational and rotational kinetic energies are changing. The rotational kinetic energy depends on the moment of inertia and the square of the angular velocity. Since the sphere is experiencing rolling and sliding, the angular velocity is not constant, and therefore, the rotational kinetic energy is not conserved. Hence, option 'c' is incorrect.
d) Angular momentum about the center of mass is conserved:
The angular momentum about the center of mass is given by the product of the moment of inertia about the center of mass and the angular velocity about the center of mass. As the sphere is experiencing both rolling and sliding motion, the angular velocity about the center of mass is changing. Therefore, the angular momentum about the center of mass is also changing and not conserved. Thus, option 'd' is incorrect.
Conclusion:
From the above analysis, we can conclude that the angular momentum of the sphere about the point of contact with the plane is conserved during the motion. Hence, option 'b' is the correct answer.
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A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the spherea)total kinetic energy is conservedb)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)angular momentum about centre of mass is conversedCorrect answer is option 'B'. Can you explain this answer?
Question Description
A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the spherea)total kinetic energy is conservedb)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)angular momentum about centre of mass is conversedCorrect 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 is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the spherea)total kinetic energy is conservedb)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)angular momentum about centre of mass is conversedCorrect 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 is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the spherea)total kinetic energy is conservedb)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)angular momentum about centre of mass is conversedCorrect answer is option 'B'. Can you explain this answer?.
A solid homogeneous sphere is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the spherea)total kinetic energy is conservedb)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)angular momentum about centre of mass is conversedCorrect 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 is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the spherea)total kinetic energy is conservedb)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)angular momentum about centre of mass is conversedCorrect 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 is moving on a rough horizontal surface, partly rolling and partly sliding. During this kind of motion of the spherea)total kinetic energy is conservedb)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)angular momentum about centre of mass is conversedCorrect answer is option 'B'. Can you explain this answer?.
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