question_answer

The moment of inertia of a rigid body, depends upon:

A) distribution of mass from axis of rotation

B) angular velocity of the body

C) angular acceleration of the body

D) mass of the body

Correct Answer: A

Solution :

Let there be a rigid body of mass M. Let the body be made up of a large number of minute particles with masses \[{{m}_{1}},\,{{m}_{2}},\,\,\,{{m}_{1}},\,......,\]and \[{{r}_{1}},\,{{r}_{2}},\,{{r}_{3}},....\] be their respective distances from the axis of rotation. Then their moments of inertia are \[{{m}_{1}}r_{1}^{2},\,{{m}_{2}}r_{2}^{2},\,{{m}_{3}}r_{3}^{2},......\] The moment of inertia of the whole body about the axis of rotation will be \[I={{m}_{1}}r_{1}^{2}+\,{{m}_{2}}r_{2}^{2}+\,{{m}_{3}}r_{3}^{3}+......\] or         \[I=\sum{m{{r}^{2}}}\] Hence, moment of inertia depends upon the distribution of mass from axis of rotation.