Match List-I with List-II:List-IList-II(A) Mo | vedclass

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(A) Using the parallel axis theorem,$I = I_{com} + MR^2$.$(A)$ For a solid sphere,$I_{com} = \frac{2}{5}MR^2$. About a tangent,$I = \frac{2}{5}MR^2 +

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$A-II, B-I, C-IV, D-III$

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(A) Using the parallel axis theorem,$I = I_{com} + MR^2$.$(A)$ For a solid sphere,$I_{com} = \frac{2}{5}MR^2$. About a tangent,$I = \frac{2}{5}MR^2 + MR^2 = \frac{7}{5}MR^2$ $(II)$.$(B)$ For a hollow sphere,$I_{com} = \frac{2}{3}MR^2$. About a tangent,$I = \frac{2}{3}MR^2 + MR^2 = \frac{5}{3}MR^2$ $(I)$.$(C)$ For a circular ring,$I_{com} = MR^2$ (about axis perpendicular to plane). By perpendicular axis theorem,$I_x + I_y = I_z$. Since $I_x = I_y = I_{diameter}$,$2I_{diameter} = MR^2$,so $I_{diameter} = \frac{1}{2}MR^2$ $(IV)$.$(D)$ For a circular disc,$I_{com} = \frac{1}{2}MR^2$. By perpendicular axis theorem,$2I_{diameter} = \frac{1}{2}MR^2$,so $I_{diameter} = \frac{1}{4}MR^2$ $(III)$.Thus,the correct matching is $A-II, B-I, C-IV, D-III$.

List-$I$	List-$II$
$(A)$ Moment of inertia of solid sphere of radius $R$ about any tangent	$(I)$ $\frac{5}{3} MR^2$
$(B)$ Moment of inertia of hollow sphere of radius $R$ about any tangent	$(II)$ $\frac{7}{5} MR^2$
$(C)$ Moment of inertia of circular ring of radius $R$ about its diameter	$(III)$ $\frac{1}{4} MR^2$
$(D)$ Moment of inertia of circular disc of radius $R$ about any diameter	$(IV)$ $\frac{1}{2} MR^2$

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