At time \( t=0 \), a disk of radius \( 1 \mathrm{~m} \) starts to roll without slipping on a hor...

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At time \( t=0 \), a disk of radius \( 1 \mathrm{~m} \) starts to roll without slipping on a horizontal plane with an angular acceleration of \( \alpha=\frac{2}{3} \mathrm{rad} \mathrm{s}^{-2} \). A small stone is stuck to the disk. At \( t=0 \), it is at the contact point of the disk and the plane. Later, at time \( t=\sqrt{\pi} s \), the stone detaches itself and flies off tangentially from the disk. The maximum height (in \( \mathrm{m} \) ) reached by the stone measured from the plane is \( \frac{1}{2}+\frac{x}{10} \). The value of \( x \) is [Take \( \left.g=10 \mathrm{~ms}^{-2}\right] \)
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