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.

A string is hanged to strong support O as shown in figure. It is wrapp

1.	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.
Answer» SOLUTION :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`