A mas m hangs with help of a string wraped around a pulley on a frictionless bearling. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is:

Options

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

Explanation

`mgR=(I+mR^(2))alpha`
`I=(1)/(2)mR^(2)`
`mg R=((3)/(2)mR^(2))alpha`
`alpha=(2g)/(3R)`
`a=Ralpha=(2g)/(3)`
OR
`alpha=(gsin theta)/(1+k^(2)//R^(2))=(g sin 90^(@))/(1+(1)/(2))=(2g)/(3)`