Question

Three rings 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

• A. 3 MR²
• B. $\frac{3}{2}MR^{2}$
• C. 5 MR²
• D. $\frac{7}{2}MR^{2}$

Answer 1

Answer: (B)

$\frac{3}{2}MR^{2}$

Answer 2

M.I of system about $YY'$ $I = I_{1} + I_{2} + I_{3}$

where I₁ = moment of inertia of ring about diameter, I₂ = I₃ = M.I. of inertia of ring about a tangent in a plane

∴ $I = \frac{1}{2}mR^{2} + \frac{3}{2}mR^{2} + \frac{3}{2}mR^{2} = \frac{7}{2}mR^{2}$