A) \[{{I}_{1}}-{{I}_{2}}\]
B) \[{{I}_{1}}+{{I}_{2}}+{{I}_{3}}+{{I}_{4}}\]
C) \[{{I}_{1}}+{{I}_{3}}\]
D) \[{{I}_{1}}+{{I}_{4}}\]
Correct Answer: A
Solution :
(a,c,d) Applying the theorem of perpendicular axis \[I={{I}_{1}}+{{I}_{2}}={{I}_{3}}+{{I}_{4}}\] Because of symmetry, we have \[{{I}_{1}}={{I}_{2}}\] and \[{{I}_{3}}={{I}_{4}}\] Hence, \[I=2{{I}_{1}}=2{{I}_{2}}=2{{I}_{3}}=2{{I}_{4}}\] or \[{{I}_{1}}={{I}_{2}}={{I}_{3}}={{I}_{4}}\] ie, sum of two moment of inertia of square plate about any axis in a plane (passing through centre) should be equal to moment of inertia about the axis passing through the centre ad perpendicular to the plane of the plate.You need to login to perform this action.
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