Problem $1.$ The double pulley shown in Figure $1$ has a mass of $3$ kg and a radius of gyration of $100$ mm $.$ The cords of negligible mass are wrapped around its inner hub and outer rim $A($end of cord connect to C is fixed$).$ Assuming there is no slippage between cords and pulleys, for a force $P=24N,$ determine using the dynamic equilibrium $($inertia$)$ method, Hint: it is convenient to take the sum of all moments about point O $.$

a$.$ Angular acceleration of the pulley $(10$ marks$)$

b$.$ Linear acceleration of the centre of the pulley $(10$ marks$),$ and

c$.$ Tension on the fixed side $($C$-$side$)$ of the cord, $(5$ marks$)$

$(25$ marks$)$