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A solid cylinder of length L and radius R has a weight W. Two cords are wrapped around the cylinder, one near each end, and the cord ends are attached to hooks on the ceiling. The cylinder is held horizontally with the two cords exactly vertical and is then released (Fig). Find (a) the tension in each cord as they unwind and (b) the linear acceleration of the cylinder as it falls.

A solid cylinder of length L and radius R has a weight W. Two cords  are wrapped  around  the cylinder,  one near each end, and the cord ends are attached to hooks on the ceiling.  The cylinder is held horizontally  with the two cords exactly vertical and is then released  (Fig). Find (a) the tension  in each cord as they unwind and (b) the linear acceleration  of the cylinder as it falls.

Grade:upto college level

3 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
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Adarsh
733 Points
6 years ago
ma=mg-2T --------------(1)
As the tension on both the cords are same.
Net torque,
\tau=\tau1+\tau2=2rT=Iα
2rT=1/2(mr2)a/r=1/2mra
T=1/4(ma)
(1) => ma=mg-2(1/4(ma))
     a=2/3g
T=1/4(m(2/3g))
T=1/6(mg)
 =W/6
 
 
Adarsh
733 Points
6 years ago
If my answer is correct please approve.
 

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