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A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved by
- a)The solid sphere
- b)The hollow sphere
- c)The disc
- d)All will achieve same kinetic energy.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A solid sphere, a hollow sphere and a disc, all having same mass and r...
Using Newton’s second law of motion, we get
Mgsinθ – μMgcosθ = Ma
So, a = gsinθ – μgcosθ which means that acceleration is independent of mass and since s = ½ at2 so t is same.
Mgsinθ – μMgcosθ = Ma
So, a = gsinθ – μgcosθ which means that acceleration is independent of mass and since s = ½ at2 so t is same.
Most Upvoted Answer
A solid sphere, a hollow sphere and a disc, all having same mass and r...
Explanation:
When the objects are released from the top of the incline, they will start rolling down due to the force of gravity. However, since the friction coefficients between the objects and the incline are not sufficient to allow pure rolling, there will be slipping between the objects and the incline.
Factors affecting kinetic energy:
The kinetic energy of an object rolling down an incline depends on several factors, including the moment of inertia and the velocity of the object. The moment of inertia depends on the mass distribution of the object, while the velocity depends on the acceleration due to gravity and the distance traveled along the incline.
Analysis of each object:
Let's analyze each object and determine how these factors affect their kinetic energy at the bottom of the incline.
Solid sphere:
The solid sphere has all its mass concentrated at its center, resulting in a smaller moment of inertia compared to the other objects. This means it requires less rotational energy to roll down the incline. However, since there is slipping, some of the rotational energy will be converted into kinetic energy of translation, resulting in a higher kinetic energy at the bottom of the incline.
Hollow sphere:
The hollow sphere has a larger moment of inertia compared to the solid sphere due to its mass distributed away from the center. This means it requires more rotational energy to roll down the incline. However, since there is slipping, some of the rotational energy will also be converted into kinetic energy of translation, resulting in a higher kinetic energy at the bottom of the incline.
Disc:
The disc has the largest moment of inertia among the three objects due to its mass distributed farthest from the center. This means it requires the most rotational energy to roll down the incline. However, since there is slipping, some of the rotational energy will also be converted into kinetic energy of translation, resulting in a higher kinetic energy at the bottom of the incline.
Conclusion:
Since all three objects experience slipping and some of their rotational energy is converted into kinetic energy of translation, they will all achieve the same kinetic energy at the bottom of the incline. Therefore, the correct answer is option D - all will achieve the same kinetic energy.
When the objects are released from the top of the incline, they will start rolling down due to the force of gravity. However, since the friction coefficients between the objects and the incline are not sufficient to allow pure rolling, there will be slipping between the objects and the incline.
Factors affecting kinetic energy:
The kinetic energy of an object rolling down an incline depends on several factors, including the moment of inertia and the velocity of the object. The moment of inertia depends on the mass distribution of the object, while the velocity depends on the acceleration due to gravity and the distance traveled along the incline.
Analysis of each object:
Let's analyze each object and determine how these factors affect their kinetic energy at the bottom of the incline.
Solid sphere:
The solid sphere has all its mass concentrated at its center, resulting in a smaller moment of inertia compared to the other objects. This means it requires less rotational energy to roll down the incline. However, since there is slipping, some of the rotational energy will be converted into kinetic energy of translation, resulting in a higher kinetic energy at the bottom of the incline.
Hollow sphere:
The hollow sphere has a larger moment of inertia compared to the solid sphere due to its mass distributed away from the center. This means it requires more rotational energy to roll down the incline. However, since there is slipping, some of the rotational energy will also be converted into kinetic energy of translation, resulting in a higher kinetic energy at the bottom of the incline.
Disc:
The disc has the largest moment of inertia among the three objects due to its mass distributed farthest from the center. This means it requires the most rotational energy to roll down the incline. However, since there is slipping, some of the rotational energy will also be converted into kinetic energy of translation, resulting in a higher kinetic energy at the bottom of the incline.
Conclusion:
Since all three objects experience slipping and some of their rotational energy is converted into kinetic energy of translation, they will all achieve the same kinetic energy at the bottom of the incline. Therefore, the correct answer is option D - all will achieve the same kinetic energy.
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A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer?.
A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer?.
Solutions for A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
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A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved bya)The solid sphereb)The hollow spherec)The discd)All will achieve same kinetic energy.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 11 tests.
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