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  4. A solid sphere of radius R has moment of inertia I about its geometrical axis. If it is melted into a disc of radius r and thickness t . If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to I , then the value of r is equal to <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-yezk0mfrnp2jv4fn.jpg />

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Q. A solid sphere of radius $R$ has moment of inertia $I$ about its geometrical axis. If it is melted into a disc of radius $r$ and thickness $t$ . If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to $I$ , then the value of $r$ is equal to
Question

NTA AbhyasNTA Abhyas 2022

Solution:

$\frac{2}{5}MR^{2}=\frac{1}{2}Mr^{2}+Mr^{2}$
or $\frac{2}{5} \, MR^{2}=\frac{3}{2}Mr^{2}$
$\therefore $ $r=\frac{2}{\sqrt{15}}R$