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A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,
- a)Speed and time of descent will be same
- b)Speed will be same, but time of descent will be different
- c)Speed will be different, but time of descent will be same
- d)Speed and time of descent both are different
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A solid sphere rolls down two different inclined planes of same heigh...
The answer is option 'B': Speed will be same, but time of descent will be different.
Explanation:
When a solid sphere rolls down an inclined plane, both its translational and rotational motion come into play. Let's consider the two inclined planes of the same height but different inclinations:
Inclined Plane 1:
The first inclined plane has a smaller inclination, which means it is less steep compared to the second inclined plane. Since the height of the inclined planes is the same, the potential energy at the top of both planes will be the same.
Since the sphere is initially at rest, its potential energy is converted into kinetic energy as it rolls down. The kinetic energy is shared between the translational kinetic energy (related to the sphere's linear motion) and rotational kinetic energy (related to the sphere's spinning motion).
- Speed: The speed of the sphere at the bottom of the inclined plane will be the same for both cases. This is because the potential energy at the top is the same, and the total kinetic energy (translational + rotational) will be equal to the initial potential energy.
- Time of Descent: The time taken by the sphere to roll down will be different for the two inclined planes. This is because the sphere needs to cover a longer distance on the inclined plane with a smaller inclination compared to the steeper inclined plane. The sphere will take more time to cover the longer distance on the less steep inclined plane compared to the steeper inclined plane.
Therefore, the speed of the sphere will be the same for both inclined planes, but the time of descent will be different.
Explanation:
When a solid sphere rolls down an inclined plane, both its translational and rotational motion come into play. Let's consider the two inclined planes of the same height but different inclinations:
Inclined Plane 1:
The first inclined plane has a smaller inclination, which means it is less steep compared to the second inclined plane. Since the height of the inclined planes is the same, the potential energy at the top of both planes will be the same.
Since the sphere is initially at rest, its potential energy is converted into kinetic energy as it rolls down. The kinetic energy is shared between the translational kinetic energy (related to the sphere's linear motion) and rotational kinetic energy (related to the sphere's spinning motion).
- Speed: The speed of the sphere at the bottom of the inclined plane will be the same for both cases. This is because the potential energy at the top is the same, and the total kinetic energy (translational + rotational) will be equal to the initial potential energy.
- Time of Descent: The time taken by the sphere to roll down will be different for the two inclined planes. This is because the sphere needs to cover a longer distance on the inclined plane with a smaller inclination compared to the steeper inclined plane. The sphere will take more time to cover the longer distance on the less steep inclined plane compared to the steeper inclined plane.
Therefore, the speed of the sphere will be the same for both inclined planes, but the time of descent will be different.
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Community Answer
A solid sphere rolls down two different inclined planes of same heigh...
In pure rolling, mechanical energy remains conserved. Therefore, when heights of inclines are equal, speed of sphere will be same in both the cases. But as acceleration down the plane, a ∝ sinθ therefore, acceleration and time of descent will be different
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A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,a)Speed and time of descent will be sameb)Speed will be same, but time of descent will be differentc)Speed will be different, but time of descent will be samed)Speed and time of descent both are differentCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,a)Speed and time of descent will be sameb)Speed will be same, but time of descent will be differentc)Speed will be different, but time of descent will be samed)Speed and time of descent both are differentCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,a)Speed and time of descent will be sameb)Speed will be same, but time of descent will be differentc)Speed will be different, but time of descent will be samed)Speed and time of descent both are differentCorrect answer is option 'B'. Can you explain this answer?.
A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,a)Speed and time of descent will be sameb)Speed will be same, but time of descent will be differentc)Speed will be different, but time of descent will be samed)Speed and time of descent both are differentCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,a)Speed and time of descent will be sameb)Speed will be same, but time of descent will be differentc)Speed will be different, but time of descent will be samed)Speed and time of descent both are differentCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere rolls down two different inclined planes of same height, but of different inclinations. In both cases,a)Speed and time of descent will be sameb)Speed will be same, but time of descent will be differentc)Speed will be different, but time of descent will be samed)Speed and time of descent both are differentCorrect answer is option 'B'. Can you explain this answer?.
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