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  • A disc and a spherical shell rotating about an. axis passing through their centers have radius of gyration in the ratio <img alt="\frac{1}{2}" src="https://entrancecorner.oncodecogs.com/gif.latex?%

A disc and a spherical shell rotating about an. axis passing through their centers have radius of gyration in the ratio \frac{1}{2}. find the ratio of the ir respective radii, assuming axis of rotation is perpendicular to the plane of the disc.

Option: 1

\frac{1}{\sqrt{3}}


Option: 2

\frac{1}{\sqrt{2}}


Option: 3

\frac{2}{\sqrt3}


Option: 4

\sqrt \frac{3}{2}


Answers (1)

best_answer

let, disc and spherical shell have massses m1,m2 respectively and their radius is 'r'

\begin{aligned} I_{\text {disc }} & =\frac{1}{2} m_1 r_1^2 \\ m_1 k_1^2 & =\frac{1}{2} m_1 r_1^2 \\ k_1 & =\frac{r_1}{\sqrt{2}} \\ I_{\text {shell }} & =\frac{2}{3} m_2 r_2^2 \\ m_2 k_2^2 & =\frac{2}{3} m_2 r_2^2 \\ K_2 & =\sqrt{\frac{2}{3} r_2} \end{aligned}

\begin{aligned} & \frac{k_1}{k_2}=\frac{1}{2} \\ & \frac{r_1}{\sqrt{2}} \times \frac{\sqrt{3}}{\sqrt{2} r_2}=\frac{1}{\2} \\ & \frac{r_1}{r_2}=\frac{1}{\sqrt{3}} \end{aligned}

Posted by

Pankaj Sanodiya

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