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

$$ma=2mg$$

$$\Rightarrow a=g/2$$