Q170 / 180 · KCET 2018 · Physics
Moment of inertia of a body about two perpendicular axes \( X \) and \( Y \) in the plane of lamina are
\( 20 \mathrm{Kg} m^{2} \) and \( 25 \mathrm{Kg} m^{2} \) respectively. Its moment of inertia about an axis perpendicular to the
plane of the lamina and passing through the point of intersection of \( X \) and \( Y \) axes is
\( 20 \mathrm{Kg} m^{2} \) and \( 25 \mathrm{Kg} m^{2} \) respectively. Its moment of inertia about an axis perpendicular to the
plane of the lamina and passing through the point of intersection of \( X \) and \( Y \) axes is
- A\( 5 \mathrm{Kg} m^{2} \)
- Correct answerB\( 45 \mathrm{Kg} m^{2} \)
- C\( 12.5 \mathrm{Kg} m^{2} \)
- D\( 500 \mathrm{Kg} m^{2} \)
Solution
Given, moment of inertia of body about \( X \) axis \( I_{X}=20 \mathrm{kgm}^{2} \)
Moment of inertia of body about \( Y \) axis \( =I_{Y}=25 \mathrm{kgm}^{2} \)
Then by perpendicular axis theorem, moment of inertia about an axis perpendicular to the plane is the sum of the
moments of inertia of two perpendicular axes through the same point. Therefore
\[ I_{Z}=I_{X}+I_{Y}=(20+25) \mathrm{kgm}^{2}=45 \mathrm{kgm}^{2} \]
Hence, moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of
intersection of \( X \) and \( Y \) axes is \( 45 \mathrm{kgm}^{2} \)
Moment of inertia of body about \( Y \) axis \( =I_{Y}=25 \mathrm{kgm}^{2} \)
Then by perpendicular axis theorem, moment of inertia about an axis perpendicular to the plane is the sum of the
moments of inertia of two perpendicular axes through the same point. Therefore
\[ I_{Z}=I_{X}+I_{Y}=(20+25) \mathrm{kgm}^{2}=45 \mathrm{kgm}^{2} \]
Hence, moment of inertia about an axis perpendicular to the plane of the lamina and passing through the point of
intersection of \( X \) and \( Y \) axes is \( 45 \mathrm{kgm}^{2} \)
Hence, the correct answer is option: 'B'.