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A cylinder of mass M, length L and radiu...

A cylinder of mass M, length L and radius R has two cords wound around it with their ends attached to the ceiling, as shown in the figure. The cylinder is held horizontally with the two cords vertical. When the system is released from rest, the linear acceleration of the cylinder as it falls will be

Text Solution

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The rod rotates and translates while falling down.

`Mg-2T=Ma` (translational motion)
`2TR=Ialpha` (Rotational motion)
Since `I=(MR^(2))/(2)` and `alpha=(a)/(R )` on solving the above equation we get `a=(2g)/(3)` and `T=(Mg)/(6)`
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