A mass ‘m’ is supported by a massless string wound around 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 ?

Options

A. `(5g)/(6)`
B. g
C. `(2g)/(3)`
D. `(g)/(2)`

Answer

D

Explanation

Equations of motion of the body

`T= mg -ma`
`Txx R = I alpha`
`TR sin 90^(@) =mR^(2) alpha`
`TR = mR^(2) alpha`
But `Ralpha =` tengential acceleration `alpha _(T ) = a `mg
taking T=ma
Taking T= ma in equation (1)
ma = mg - ma
`2 a = g`
`a= (g )/(2 )`