Ratio of K. E. of solid cylinder to shell

In summary, the ratio of kinetic energy between a solid cylinder and a hollow cylinder is dependent on their respective masses and velocities. When the mass of the cylinders is doubled, the ratio of kinetic energy will also double. The shape of the cylinders does not affect the ratio of kinetic energy, but increasing the velocity will result in an increased ratio. However, the ratio of kinetic energy cannot be used to determine the type of motion of the cylinders.
  • #1
Pushoam
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Homework Statement


upload_2017-12-22_11-38-41.png


Homework Equations

The Attempt at a Solution


total kinetic energy of a rigid body = rotational kinetic energy of the body around its center of mass + translational kinetic energy of center of mass

For solid cylinder, total kinetic energy = ## \frac { [I = \frac 1 2 mR^2]\omega ^2 } 2 + \frac 1 2 mv^2 = \frac { 3 mv^2} 4;~ v = \omega R ##

Similarly for hollow cylinder , total kinetic energy = ## mv^2 ##

So, the correct opinion is (a).

Is this correct?
 

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  • #2
Pushoam said:
the correct opinion is (a).
yes.
 
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  • #3
Thanks.
 

1. What is the ratio of kinetic energy between a solid cylinder and a hollow cylinder?

The ratio of kinetic energy between a solid cylinder and a hollow cylinder is dependent on their respective masses and velocities. It can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. Therefore, the ratio will vary depending on the specific values of these variables.

2. How does the ratio of kinetic energy change when the mass of the cylinders is doubled?

The ratio of kinetic energy will also double when the mass of the cylinders is doubled, assuming that the velocities remain constant. This is because kinetic energy is directly proportional to mass.

3. Is the ratio of kinetic energy affected by the shape of the cylinders?

No, the shape of the cylinders does not affect the ratio of kinetic energy. As long as the mass and velocity of the cylinders remain the same, the ratio will also remain the same.

4. What happens to the ratio of kinetic energy when the velocity of the cylinders is increased?

If the velocity of the cylinders is increased, the ratio of kinetic energy will also increase. This is because kinetic energy is directly proportional to the square of velocity. Therefore, a higher velocity will result in a higher ratio.

5. Can the ratio of kinetic energy be used to determine the type of motion of the cylinders?

No, the ratio of kinetic energy cannot determine the type of motion of the cylinders. It only gives information about the relative amount of kinetic energy between the two cylinders. Additional information, such as the direction and forces acting on the cylinders, would be needed to determine the type of motion.

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