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STD 11 - 6. system of particles and rotational motion — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 6. system of particles and rotational motion4 Marks
Question
A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $\sqrt{\frac{2}{x}}$. The value of $x$ is $.......$
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Answer

For ring $I=m R_1^2=m K_1^2$

$\therefore$ Radius of gyration $K_1=R_1$

For solid sphere

$I^{\prime}=\frac{2}{5} m^{\prime} R_2^2=m^{\prime} K_2^2$

$\therefore \text { Its radius of gyration }=K_2=\sqrt{\frac{2}{5}} R_2$

$\because K_1=K_2$

$\therefore R_1=\sqrt{\frac{2}{5}} R_2$

$\therefore \frac{R_1}{R_2}=\sqrt{\frac{2}{5}}$

$\therefore x=5$

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