A string is hanged to strong support O as shown in figure. It is wrapped to a disc of mass m and radius R at its other end. This string is weightless and unstretchable then find the linear acceleration of centre of mass of disc.

Explanation

Tension produced in the string is shown in figure. Linear equation of motion of disc is
`ma=mg-T`
`therefore T=m(g-a)….(1)`
If angular acceleration of disc `alpha`, then
`Ia=TR…..(2)`
but `alpha=(a)/(R )` for disc,
`I=(mR^(2))/(2)`
`therefore (mR^(2))/(2).(a)/(R)=m(g-a)R`
Putting value of T from equation (1)
`therefore (a)/(2)=g-a`
`therefore (3)/(2)a=g`
`therefore a=2//3g`