Question

A wire frame AOPQB is free to rotate about a vertical axis passing through C ⊥ to plane of AOPQB. The mass M of the frame is uniformly distributed over its whole length. What is the moment of inertia of the frame about this axis, if OA = QB = r and CP = r (the radius of semicircular part )

• A. Mr²$\left( \frac { 14 + 3 \pi } { 3 \pi + 6 } \right)$
• B. Mr²$\left( \frac { \pi + r } { \pi + 2 r } \right)$
• C. Mr² $\left( \frac { 3 } { 4 } \pi \right)$
• D. $\frac { 1 } { 2 }$Mr²

Answer 1

Answer: (A)

Mr²$\left( \frac { 14 + 3 \pi } { 3 \pi + 6 } \right)$

Answer 2

M.I. = M.I. of OA + M.I of Q.B. + M.I. of semicircular region = 2

2 ⋅ = Mr² $\left( \frac { 14 + 3 \pi } { 3 \pi + 6 } \right)$

(1) is the correct.