question_answer

The moment of inertia of a circular disc of radius\[2\text{ }m\]and mass \[2\text{ }kg,\] about an axis passing through its centre of mass is\[2\text{ }kg-{{m}^{2}}\]. Its moment of inertia about an axis parallel to this axis and passing through its edge (in\[kg-{{m}^{2}}\]) is

A)  \[10\]

B)  \[8\]

C)  \[6\]              

D)  \[4\]

Correct Answer: A

Solution :

Moment of inertia about \[XX',\] \[{{I}_{XX'}}=2\,kg-{{m}^{2}}\] Moment of inertia about the given axis ie, about \[YY',\] \[{{I}_{YY'}}={{I}_{XX'}}+M{{R}^{2}}\] \[=2+2\times {{(2)}^{2}}\] \[=2+8\] \[=10\,kg-{{m}^{2}}\]