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A disk of mass m on a frictionless table is attached to a hanging cylinder of mass M by a cord through a hole in the table (see Fig). Find the speed with which the disk must move in a circle of radius r for the cylinder to stay at rest.

A disk of mass m on a frictionless table is attached to a hanging cylinder of mass M by a cord through a hole in the table (see Fig). Find the speed with which the disk must move in a circle of radius r for the cylinder to stay at rest.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago

The free body diagram of the rotating disk is: 234-2022_1.PNG
It can be seen from the diagram that the centripetal force to the disk must be provided by the tension in the cord, therefore
234-55_1.PNG
The free body diagram of the cylinder is shown below:

234-801_1.PNG
For the cylinder to stay at rest, the tension in the cord should be equal to its weight, that is T = W.

234-871_1.PNG
Here g is the acceleration due to gravity.
Therefore the speed with which the disk should rotate to keep the cylinder at rest is given by expression234-158_1.PNG

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