Solid sphere and hollow sphere rolled down an inclined plane

In summary, when a solid sphere and a hollow one of the same mass and radii are rolled down a rough inclined plane, the solid sphere reaches the bottom with a greater speed. This is because both spheres experience the same acceleration due to gravity, but the solid sphere has a greater mass, leading to a higher kinetic energy. However, the statement does not provide enough information to determine if option B is also correct.
  • #1
Yatin
20
1
A solid sphere and a hollow one of same mass and radii are rolled down a rough inclined plane.
Which of the following is true?
(A) solid sphere reaches bottom with greater speed.
(B) solid sphere reaches the bottom with greater kinetic energy.

( I know that option A is correct.Thus I felt that B should also be correct.
However A is the only option given in the book as correct. Please help)
 
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  • #2
Why do you think the kinetic energy of the solid sphere is greater? Because of its higher velocity? If this is the case, maybe another look at the statement helps: it says ' [...] are rolled down [...] '.
 
  • #3
See the above but even in that case V at the end = V initial + the acceleration due to gravity that is experienced by both balls; or, is there something else I am also missing?
 
Last edited:
  • #4
Please use the template so we can help you.
 

Related to Solid sphere and hollow sphere rolled down an inclined plane

1. What is the difference between a solid sphere and a hollow sphere rolled down an inclined plane?

A solid sphere is a three-dimensional object with a uniform density throughout, while a hollow sphere is a three-dimensional object with a hollow interior and a solid outer layer. When rolled down an inclined plane, a solid sphere will have a higher moment of inertia and will roll slower than a hollow sphere.

2. How does the angle of the inclined plane affect the rolling motion of a solid sphere and a hollow sphere?

The steeper the angle of the inclined plane, the faster both a solid and a hollow sphere will roll. However, because a solid sphere has a higher moment of inertia, it will roll slower than a hollow sphere at the same angle.

3. What is the relationship between the mass of a sphere and its rolling speed down an inclined plane?

The mass of a sphere does not directly affect its rolling speed down an inclined plane. However, a heavier sphere will have a higher moment of inertia and will therefore roll slower than a lighter sphere.

4. Can a hollow sphere roll faster than a solid sphere down an inclined plane?

Yes, a hollow sphere can roll faster than a solid sphere down an inclined plane because it has a lower moment of inertia. This means that it requires less energy to rotate and therefore can roll faster.

5. How does the surface material of the inclined plane affect the rolling motion of a solid and a hollow sphere?

The surface material of an inclined plane can affect the rolling motion of a solid and a hollow sphere by providing different levels of friction. A rough surface will slow down the rolling speed of both spheres, while a smooth surface will allow for faster rolling. However, a solid sphere will still have a higher moment of inertia and will roll slower than a hollow sphere on any type of surface.

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