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A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of mass
- a)h = R
- b)h = 2 R
- c)h = 0
- d)The acceleration will be same whatever h may be
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A solid sphere of radius R is placed on a smooth horizontal surface. A...
The linear acceleration of Centre of mass will be a =F/m, wherever the force is applied. Hence, the acceleration will be same whatever the value of h may be.
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A solid sphere of radius R is placed on a smooth horizontal surface. A...
Explanation:
The acceleration of the center of mass of a solid sphere on a smooth horizontal surface will be the same, irrespective of the height at which the force is applied. This can be explained by the following points:
- The center of mass of a solid sphere is located at its geometric center. Therefore, the force applied at any height on the sphere will produce the same torque about the center of mass.
- The torque produced by the force will cause the sphere to rotate about its center of mass. The angular acceleration of the sphere is given by the torque divided by the moment of inertia of the sphere.
- The moment of inertia of a solid sphere is given by (2/5)MR^2, where M is the mass of the sphere and R is its radius. Therefore, the angular acceleration of the sphere is directly proportional to the force applied and inversely proportional to the height at which it is applied.
- However, the linear acceleration of the center of mass is related to the angular acceleration by the formula a = αR, where α is the angular acceleration and R is the radius of the sphere. Therefore, the linear acceleration of the center of mass is independent of the height at which the force is applied.
- Thus, the acceleration of the center of mass of a solid sphere on a smooth horizontal surface will be the same, irrespective of the height at which the force is applied.
Therefore, option D is the correct answer.
The acceleration of the center of mass of a solid sphere on a smooth horizontal surface will be the same, irrespective of the height at which the force is applied. This can be explained by the following points:
- The center of mass of a solid sphere is located at its geometric center. Therefore, the force applied at any height on the sphere will produce the same torque about the center of mass.
- The torque produced by the force will cause the sphere to rotate about its center of mass. The angular acceleration of the sphere is given by the torque divided by the moment of inertia of the sphere.
- The moment of inertia of a solid sphere is given by (2/5)MR^2, where M is the mass of the sphere and R is its radius. Therefore, the angular acceleration of the sphere is directly proportional to the force applied and inversely proportional to the height at which it is applied.
- However, the linear acceleration of the center of mass is related to the angular acceleration by the formula a = αR, where α is the angular acceleration and R is the radius of the sphere. Therefore, the linear acceleration of the center of mass is independent of the height at which the force is applied.
- Thus, the acceleration of the center of mass of a solid sphere on a smooth horizontal surface will be the same, irrespective of the height at which the force is applied.
Therefore, option D is the correct answer.
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A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer?
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A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer?.
A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer?.
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A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A solid sphere of radius R is placed on a smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of the Centre of massa)h = Rb)h = 2 Rc)h = 0d)The acceleration will be same whatever h may beCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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