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.
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