Find the moment of inertia of a spherical ball of mass m and radius r attached at the end of a thin straight rod of mass M and length L about the axis AA’ shown in the figure.

Q: Find the moment of inertia of a spherical ball of mass m and radius r attached at the end of a thin straight rod of mass M and length L about the axis AA’ shown in the figure.

Numerical

(a) $\displaystyle \frac{L^2}{2}(m + \frac{M}{3}) + \frac{2}{5}m r^2 $

(b) $\displaystyle L^2(m + \frac{M}{3}) + \frac{2}{5}m r^2 $

(c) $\displaystyle \frac{2 L^2}{3}(m + \frac{M}{3}) + \frac{2}{5}m r^2 $

(d) None of these

Ans: (b)