A body of mass `5 kg` is attached to a weightless string wound round a cylinder of mass `8 kg` and radius `0.3 m`. The body is allowed to fall. Calculate (i) tension in the string, (ii) acceleration with which the body falls and (iii) angular acceleration of the cylinder.

Explanation

Here, `m = 5 kg, M = 8kg, R = 0.3 m`
Moment of inertia of the cylinder `I = (1)/(2)MR^(2)`
(i) Tension in the string, `T = (mg)/(1 + mR^(2)//I)`
`= (mg)/(1 + (2mR^(2))/(MR^(2))) = (mg)/(1+(2m)/(M)) = (5 xx 9.8)/(1+ (2 xx 5)/(8)) = 21.78 N`
(ii) Linear acceleration
`a = (g)/(1 + I//mR^(2)) = (g)/(1+ (M)/(2m)) = (9.8)/(1 + (8)/(2xx5))`
`= 5.44 m//s^(2)`
(iii) Angular acceleration,
`alpha = (a)/(R ) = (5.44)/(0.3) = 18.13 rad//s^(2)`