Three solid spheres each of mass ' $M$ ' and radius ' $R$ ' are arranged as shown in the figure. The moment…
Three solid spheres each of mass ' $M$ ' and radius ' $R$ ' are arranged as shown in the figure. The moment of inertia of the system about YY' will be
$\frac{16}{5} \mathrm{MR}^2$
$\frac{21}{5} \mathrm{MR}^2$
$\frac{7}{5} \mathrm{MR}^2$
$\frac{11}{5} \mathrm{MR}^2$
Solution
Moment of inertia of the upper sphere $=\frac{2}{5} \mathrm{MR}^2$
For each lower sphere M.I. $=\frac{2}{5} \mathrm{MR}^2+\mathrm{MR}^2=\frac{7}{5} \mathrm{MR}^2$
$\therefore$ Total moment of inertia $\mathrm{I}=\frac{2}{5} \mathrm{MR}^2+2 \times \frac{7}{5} \mathrm{MR}^2=\frac{16}{5} \mathrm{MR}^2$
