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  4. A coin placed on a gramophone record rotating at 33 rpm flies off the record, if it is placed at a distance of more than 16 cm from the axis of rotation. If the record is revolving at 66 rpm, the coin will fly off if it is placed at a distance not less than

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Q. A coin placed on a gramophone record rotating at 33 rpm flies off the record, if it is placed at a distance of more than 16 cm from the axis of rotation. If the record is revolving at 66 rpm, the coin will fly off if it is placed at a distance not less than

System of Particles and Rotational Motion

Solution:

$m \omega^{2} r_{\text {max }}=\mu \,mg$
$\Rightarrow m\left(4 \pi^{2} f^{2}\right) r_{\max }=\mu \,m g$
Also, $m\left(4 \pi^{2} f^{\prime 2}\right) r_{\max }^{\prime}=\mu mg$
$\Rightarrow f^{2} r_{\max }=f^{\prime 2} r_{\max }^{\prime}$
$ \Rightarrow r_{\max }^{\prime} =\left(\frac{f}{f^{\prime}}\right)^{2} r_{\max }=\left(\frac{33 rpm }{66 rpm }\right)^{2}(16 \,cm )$
$=\frac{1}{4}(16 \,cm )=4\, cm $