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July 2, 2017

Mass supported by a Hollow Cylinder

Let's discuss a beautiful problem useful for Physics Olympiad based on Mass supported by a Hollow Cylinder.

The Problem: 

A mass m is supported by a massless string wound on a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

Solution:

For the mass m, the force equation stands as:

$$mg-T=ma....(i)$$

For the cylinder, the force equation is:

$$ T.R=mR^2(a/R)$$

Hence,

from above equation $$ T=ma $$

Now, putting the value of T in equation (i), we get

$$ma=2mg$$

$$\Rightarrow a=g/2$$

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