Question

Three solid spheres, each of mass $m$ and radius $l$, are placed at the corners of an equilateral triangle of side $2l$. The moment of inertia of this system about an axis along one of side of the triangle is :

• A. ${3ml}^2$
• B. $\frac{65}{5}{ml}^2$
• C. $\frac{33}{4}{ml}^2$
• D. $\frac{21}{5}{ml}^2$

Answer 1

The correct option is D $\frac{21}{5}{ml}^2$

REF.Image

$I_C=I_B=\frac{2}{5}m{l}^2$

Moment of inertia of sphere as A about an axis from A will be $\frac{2}{5}m{l}^2$

but the axis BC is at separation $x=\sqrt{3}l$

so about BC will be $\frac{2}{5}m{l}^2+m{x}^2$

$\Rightarrow I_A=\frac{2}{5}m{l}^2+3m{l}^2$

$I_A=\frac{17m{l}^2}{5}$

Net $I=I_A+I_B+I_C=\frac{21m{l}^2}{5}$