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A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]
- a)Solid sphere
- b)Hollow sphere
- c)Ring
- d)All same
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A solid sphere, a hollow sphere and a ring are released from top of an...
As the plane is frictionless, thus there will be only slipping and no rolling. So, for all of them acceleration will be ‘gsinθ’
Most Upvoted Answer
A solid sphere, a hollow sphere and a ring are released from top of an...
Explanation:
When a solid sphere, a hollow sphere, and a ring are released from the top of an inclined plane, they start sliding down the plane. Since the plane is frictionless, there is no rolling motion. The acceleration of each object is given by the following formula:
a = g.sinθ
where g is the acceleration due to gravity and θ is the angle of inclination of the plane.
Analysis:
Let's compare the acceleration of each object and see which one has the maximum acceleration.
1. Solid sphere:
The solid sphere has a uniform mass distribution, and its moment of inertia is given by:
I = 2/5 MR²
where M is the mass of the sphere and R is the radius of the sphere.
Since there is no rolling motion, the torque acting on the sphere is zero. Therefore, we can apply the following equation of motion:
F = ma
where F is the net force acting on the sphere, and a is its acceleration.
The net force acting on the sphere is given by:
F = Mg.sinθ
where Mg is the weight of the sphere.
Substituting the values of F and a, we get:
a = g.sinθ
Therefore, the acceleration of the solid sphere is independent of its mass and radius.
2. Hollow sphere:
The hollow sphere has all its mass concentrated at the surface, and its moment of inertia is given by:
I = 2/3 MR²
where M is the mass of the sphere and R is the radius of the sphere.
Using the same equation of motion and net force as for the solid sphere, we get:
a = g.sinθ
Therefore, the acceleration of the hollow sphere is also independent of its mass and radius.
3. Ring:
The ring also has all its mass concentrated at the surface, and its moment of inertia is given by:
I = MR²
Using the same equation of motion and net force as for the solid and hollow spheres, we get:
a = g.sinθ
Therefore, the acceleration of the ring is also independent of its mass and radius.
Conclusion:
Hence, we can conclude that the maximum acceleration down the plane is the same for all three objects, and it is given by:
a = g.sinθ
Therefore, the correct answer is option D, i.e., all three objects have the same maximum acceleration down the plane.
When a solid sphere, a hollow sphere, and a ring are released from the top of an inclined plane, they start sliding down the plane. Since the plane is frictionless, there is no rolling motion. The acceleration of each object is given by the following formula:
a = g.sinθ
where g is the acceleration due to gravity and θ is the angle of inclination of the plane.
Analysis:
Let's compare the acceleration of each object and see which one has the maximum acceleration.
1. Solid sphere:
The solid sphere has a uniform mass distribution, and its moment of inertia is given by:
I = 2/5 MR²
where M is the mass of the sphere and R is the radius of the sphere.
Since there is no rolling motion, the torque acting on the sphere is zero. Therefore, we can apply the following equation of motion:
F = ma
where F is the net force acting on the sphere, and a is its acceleration.
The net force acting on the sphere is given by:
F = Mg.sinθ
where Mg is the weight of the sphere.
Substituting the values of F and a, we get:
a = g.sinθ
Therefore, the acceleration of the solid sphere is independent of its mass and radius.
2. Hollow sphere:
The hollow sphere has all its mass concentrated at the surface, and its moment of inertia is given by:
I = 2/3 MR²
where M is the mass of the sphere and R is the radius of the sphere.
Using the same equation of motion and net force as for the solid sphere, we get:
a = g.sinθ
Therefore, the acceleration of the hollow sphere is also independent of its mass and radius.
3. Ring:
The ring also has all its mass concentrated at the surface, and its moment of inertia is given by:
I = MR²
Using the same equation of motion and net force as for the solid and hollow spheres, we get:
a = g.sinθ
Therefore, the acceleration of the ring is also independent of its mass and radius.
Conclusion:
Hence, we can conclude that the maximum acceleration down the plane is the same for all three objects, and it is given by:
a = g.sinθ
Therefore, the correct answer is option D, i.e., all three objects have the same maximum acceleration down the plane.
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Community Answer
A solid sphere, a hollow sphere and a ring are released from top of an...
Because of there is no rolling so we have not to use the formula of the rotational inclined acceleration. It will simply be gsin@ for all these.
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A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]a)Solid sphereb)Hollow spherec)Ringd)All sameCorrect answer is option 'D'. Can you explain this answer?
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A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]a)Solid sphereb)Hollow spherec)Ringd)All sameCorrect answer is option 'D'. Can you explain this answer? for Class 11 2024 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 ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]a)Solid sphereb)Hollow spherec)Ringd)All sameCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]a)Solid sphereb)Hollow spherec)Ringd)All sameCorrect answer is option 'D'. Can you explain this answer?.
A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]a)Solid sphereb)Hollow spherec)Ringd)All sameCorrect answer is option 'D'. Can you explain this answer? for Class 11 2024 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 ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]a)Solid sphereb)Hollow spherec)Ringd)All sameCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) [AIEEE 2002]a)Solid sphereb)Hollow spherec)Ringd)All sameCorrect answer is option 'D'. Can you explain this answer?.
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