question_answer

Point masses 1, 2, 3 and 4 kg are lying at the points (0,0,0), (2,0,0), (0,3,0) and (-2, -2,0) respectively. The moment of inertia of this system about X-axis will be

A) \[43\,kg\,{{m}^{2}}\]

B) \[34\,kg\,{{m}^{2}}\]

C) \[27\,kg\,{{m}^{2}}\]

D) \[72\,kg\,{{m}^{2}}\]

Correct Answer: A

Solution :

[a] Moment of inertia of the whole system about the axis of rotation will be equal to the sum of the moments of inertia of all the particles. \[\therefore \,I={{I}_{1}}+{{I}_{2}}+{{I}_{3}}+{{I}_{4}}\] \[=0+0+27+16=43\,kg\,{{m}^{2}}\]