A solid hemisphere and a hemispherical shell | vedclass

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Question

(A) The moment of inertia of a solid hemisphere of mass $M_s$ about its diameter is $I_s = \frac{2}{5} M_s R^2$.Here,the mass of the solid hemisphere

Vedclass · Accepted Answer

$\frac{8 mR^2}{15}$

Vedclass · Answer

(A) The moment of inertia of a solid hemisphere of mass $M_s$ about its diameter is $I_s = \frac{2}{5} M_s R^2$.Here,the mass of the solid hemisphere is $M_s = m/2$,so $I_s = \frac{2}{5} (m/2) R^2 = \frac{1}{5} m R^2$.The moment of inertia of a hemispherical shell of mass $M_h$ about its diameter is $I_h = \frac{2}{3} M_h R^2$.Here,the mass of the hemispherical shell is $M_h = m/2$,so $I_h = \frac{2}{3} (m/2) R^2 = \frac{1}{3} m R^2$.The total moment of inertia about the axis $AB$ is the sum of the individual moments of inertia:$I = I_s + I_h = \frac{1}{5} m R^2 + \frac{1}{3} m R^2 = \left(\frac{3+5}{15}\right) m R^2 = \frac{8}{15} m R^2$.

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

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