Consider a body whose centre of mass is situated at the origin, with three of its particles located at (a, 0, 0) , (0, a, 0) , and (0, 0, a) . The moments of inertia of this body about the X and Y axes are each 0.20 kg-m ^2 . The moment of

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Consider a body whose centre of mass is situated at the origin, with three of its particles located at (a, 0, 0) , (0, a, 0) , and (0, 0, a) . The moments of inertia of this body about the X and Y axes are each 0.20 kg-m ^2 . The moment of inertia about the Z -axis

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Correct answer: C. cannot be deduced using the given information

The moments of inertia of a body about the X , Y , and Z axes are given by: I_x = m_i (y_i^2 + z_i^2) I_y = m_i (x_i^2 + z_i^2) I_z = m_i (x_i^2 + y_i^2) Adding the moments of inertia about the X and Y axes, we get: I_x + I_y = m_i (x_i^2 + y_i^2 + 2z_i^2) I_x + I_y = m_i (x_i^2 + y_i^2) + 2 m_i z_i^2 I_x + I_y = I_z + 2 m_i z_i^2 The perpendicular axis theorem, which states I_z = I_x + I_y , is only applicable for a two-dimensional planar body (lamina) lying entirely in the XY plane, where z_i = 0 for all particle

Consider a body whose centre of mass is situated at the origin, with three of its particles located at (a, 0, 0) , (0, a, 0) , and (0, 0, a) . The moments of inertia of this body about the X and Y axes are each 0.20 kg-m ^2 . The moment of inertia about the Z -axis

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