What is the tension in a rotating chain attached to a wooden disc?

[Vibhor]

Homework Statement

A metallic chain with a length ‘l’ andd whose ends are joined together is fitted onto a wooden disc as shown in the figure.The disc rotates with a speed of n revolutions per second.Find the tension of the chain T if its mass is m.

Homework Equations

The Attempt at a Solution

Honestly I have very little idea about how to approach this problem .

All I know is that every part of the chain is undergoing centripetal acceleration as the chain is rotating .Since the speed is constant there would be no tangential acceleration.

ω = 2nπ

Please help me with this problem .

Thanks .

 

[BvU]

Well, centripetal acceleration requires a centripetal force. What can possibly be the source of that force ?
Think of a ring of people holding hands and dancing around with considerable speed. What if a hand let's go ?

 

[Vibhor]

Well, centripetal acceleration requires a centripetal force. What can possibly be the source of that force ?

Component of tension in the radial direction. But how do I find that component ?

Think of a ring of people holding hands and dancing around with considerable speed. What if a hand let's go ?

The ring will fall apart .

 

[BvU]

To find that radial component, draw a section of the chain and note that the vector sum of the tensions points just where you want it !

 

[Vibhor]

Sorry for the late response .

I still don't understand how to approach this problem.

 

[Vibhor]

Doesn't the wooden disc play any role in providing centripetal force to the chain ?

 

[BvU]

Doesn't the wooden disc play any role in providing centripetal force to the chain ?

Not really. How could it? All it can do is push radially outward (a normal force!), which doesn't help: it is in an altogether wrong direction ! Iron doesn't have a tendency to stick to wood by some physical force...

Did you draw a section of the chain and discover how the sum of the tensions working on it points in a desirable direction ?