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  • A uniform solid cylinder of mass 'm' and radius 'r' is kept in the horizontal position by winding two identical strings on its left and right end as shown in the figure. The strings

A uniform solid cylinder of mass 'm' and radius 'r' is kept in the horizontal position by winding two identical strings on its left and right end as shown in the figure. The strings are wound in the same sense and their other ends are attached to the ceiling.

A heavy mass ' M ' is attached to the middle of the cylinder by winding in the same sense in the cylinder. If the system is released from the rest, find the acceleration of the heavier mass ' M '

Option: 1

\frac{g}{3}


Option: 2

\frac{4g}{3}


Option: 3

g


Option: 4

\frac{5g}{3}


Answers (1)

best_answer

Investigating the motion of the cylinder before attaching a heavier mass to it.



m g-T =m a_{c \cdot m} \\

\gamma T =I \alpha

As the strings are not slipping over the cylinder

a=r \alpha \\

a=\left(\frac{m r^2}{m r^2+I}\right) g
As, for the solid cylinder, I=\frac{1}{2} m r^2

a=\left(\frac{mr^2}{\frac{3}{2} mr^2 }\right) g=\frac{2}{3} g

Now attaching a heavier mass to it, the acceleration of it can be given by

a_x=a+\gamma \alpha=2 a \\
a_x=\frac{4}{3} g
but this acceleration is more than ' g ' which is not possible, so heavier mass will be in the free fall after its release.

Posted by

himanshu.meshram

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