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Question

In figure the cylinder of mass 10kg and radius 10cm has a tape wrapped round it. The pulley weighs 100N and has a radius 5cm. When the system is released, the 5kg mass comes down and the cylinder rolls without slipping. Calculate the acceleration and velocity of the mass as a function of time.
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Solution

M=10kg , R1=10cm and M2g=100
For 5 kg block
5gT2=5a2 ....(1)
for pulley R2=5cm
(T2T1)R2=Iα2
(T2T1)R2=M2R222α2 ....(2)
, where M2=mass of pulley
For cylinder
T1+f=M1a1 ...(3)
torque about the cylinder
(T1f)R1=M1R212α1 ...(4)
a1=R1α1 ....(5)
Acceleration of rope at the top cylinder and over the pulley
a1+R1α1=R2α2 ...(6)
Also the acceleration of rope at the top of puller is equal to acceleration of cylinder
R2α2=a2 ...(7)
on solving all the equations
a2=4g11
and velocity v2=a2t=4gt11

689814_219427_ans_5c862fe97375420cacde839242ff270c.JPG

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