Solid Sphere :

JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 1

$$ \begin{aligned} & I_{\text {tangent }}=I_{\mathrm{cm}}+m R^{2} \\\\ & =\frac{2}{5} m R^{2}+m R^{2}=\frac{7}{5} m R^{2} \\\\ & =7 R^{2} \quad(m=5 \mathrm{~kg}) \end{aligned} $$

CIRCULAR DISC :

JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 2

$$ \begin{aligned} I_{\text {disc }} & =I_{\mathrm{cm}}+m R^{2} \\\\ & =\frac{m R^{2}}{4}+m R^{2} \\\\ & =\frac{5}{4} m R^{2} \\\\ & =5 R^{2} \end{aligned} $$

$\frac{l_{\text {disc }}}{l_{\text {tangent }}}=\frac{5}{7}$

Concept :

1. For Solid Sphere :

Position of the axis of rotation : About its diametric axis which passes through its centre of mass
JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 3

JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 3

Moment of Inertia (I) = $${2 \over 5}M{R^2}$$

Radius of gyration (K) = $$\sqrt {{2 \over 5}} R$$

Position of the axis of rotation : About a tangent to the sphere
JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 4

JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 4

Moment of Inertia (I) = $${7 \over 5}M{R^2}$$

Radius of gyration (K) = $$\sqrt {{7 \over 5}} R$$

2. For CIRCULAR DISC :

Position of the axis of rotation : About an axis perpendicular to the plane and passes through the centre
JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 5

JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 5

Moment of Inertia (I) = $${1 \over 2}M{R^2}$$

Radius of gyration (K) = $${R \over {\sqrt 2 }}$$

Position of the axis of rotation : About the diametric axis
JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 6

JEE Main 2023 (Online) 25th January Evening Shift Physics - Rotational Motion Question 90 English Explanation 6

Moment of Inertia (I) = $${1 \over 4}M{R^2}$$

Radius of gyration (K) = $${R \over { 2 }}$$

Rotational Motion

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