question_answer

Point masses of 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. \[\therefore \] \[I={{I}_{1}}+{{I}_{2}}+{{I}_{3}}+{{I}_{4}}\] \[=0+0+27+16=43\,kg\,{{m}^{2}}\]