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. $\frac{11}{5}m{l}^2$
• B. $\frac{12}{5}m{l}^2$
• C. $\frac{2}{5}m{l}^2$
• D. $\frac{21}{5}m{l}^2$

Answer 1

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

$I_1=\frac{2}{5}M{l}^2=I_2{I}_3=\frac{2}{5}M{l}^2+M\left(x^2\right)=\frac{2}{5}M{l}^2+3M{l}^2=\frac{17}{5}M{l}^2\therefore I=I_1+I_2+I_3=\frac{2}{5}M{l}^2+\frac{2}{5}M{l}^2+\frac{17}{5}M{l}^2=\frac{21}{5}M{l}^2$