question_answer

Point masses \[1,\text{ }2,-3\]and \[4\text{ }kg\]are lying at the point \[(0,0,0)\]\[(2,0,0)\]\[(0,3,0)\]  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 :

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, \[I={{I}_{1}}+{{I}_{2}}+{{I}_{3}}+{{I}_{4}}\] \[\therefore \] \[I={{m}_{1}}r_{1}^{2}+{{m}_{2}}r_{2}^{2}+{{m}_{3}}r_{3}^{2}+{{m}_{4}}r_{4}^{2}\] \[I=(1\times 0)+(2\times 0)+(3\times {{3}^{2}})+4{{(-2)}^{2}}\] \[I=0+0+27+16=43kg-{{m}^{2}}\]