Question

A hemi-spherical cavity is created in solid sphere of radius 2R and mass M as shown in the figure with centre at origin.

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Linked Question 1

The coordinate of centre of mass of the remaining system is

$(- \frac{R}{15}, - \frac{R}{40}, 0)$

$(- \frac{R}{15}, - \frac{R}{30}, 0)$

$(- \frac{R}{7}, - \frac{R}{56}, 0)$

None of these

$\frac{M}{16} (R \hat{i} + \frac{3 R}{8} \hat{j}) + \frac{15 M}{16} \vec{r} = 0$

Linked Question 2

The moment of inertia about y-axis is

$\frac{121}{80} {MR}^{2}$

None of these

$\frac{93}{80} {MR}^{2}$

$\frac{128}{5} {MR}^{2}$

$I = \frac{2}{5} M {(2 R)}^{2} - \frac{7}{5} \frac{M}{16} R^{2} = \frac{121}{80} {MR}^{2}$