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

Question

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, $ 5 \mathrm{Kg} m^{2} $, $ 45 \mathrm{Kg} m^{2} $, $ 12.5 \mathrm{Kg} m^{2} $, $ 500 \mathrm{Kg} m^{2} $

MARKS App · Accepted Answer

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} $

Search any question & find its solution

Looking for more such questions to practice?