Figure shows a composite pulley of that consist of two cylinders of 'R' and ′ 2R ′ stacked coaxially. Moment of inertia of composite pulley is 
. A light string is wound over pulley and another pulley 'A' of mass 'M' is hanged through the string as shown in figure.
(i) The composite pulley is rotated with angular velocity ' ω′ in the direction shown. The pulley 'A' will –
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Ans.
(i)
Sol. Let if pulley rotate by Pulley ’A’ moves up
by ‘x’
String required = 2R θ – R θ
= R θ
String released = 2x
∴ 2x = R θ
⇒ 2 v = R ω
∴ v = 
(ii)
Sol.
Composite pulley
T.2R – T.R = 
. α
⇒ T.R = 
. 
T = 
…. (i)
Pulley A :
Mg – 2T = Ma …. (ii)
From (i) & (ii)
∴ a = 
(iii)
Sol. Composite pulley
T 1 . 2R – T 2 R = 
⇒ 2T 1 – T 2 = 
… (i)
Pulley A :
Mg – (T 1 + T 2 ) = Ma … (ii)
(T 2 – T 1 )r = 
. 
r = radius of pulley
⇒ T 2 – T 1 = 
… (iii)
From (i), (ii) & (iii) a = 
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