question_answer

The moment of inertia of a disc of mass m and radius r about an axis, which is tangential to the circumference of the disc and parallel to its diameter is

A) \[\frac{3}{2}m\,{{r}^{2}}\]     

B)        \[\frac{2}{3}m\,{{r}^{2}}\]

C) \[\frac{5}{4}m\,{{r}^{2}}\]     

D)        \[\frac{4}{5}m\,{{r}^{2}}\]

Correct Answer: C

Solution :

[c] We know that moment of inertia of a disc about its diameter is \[=\frac{1}{4}m{{r}^{2}}.\] In the figure AB is a diameter. Which passes through centre of mass of the disc. CD is another axis which is parallel to AB and about which we shall have to calculate moment of inertia. Now, from the theory of parallel axis \[I={{I}_{g}}+m{{d}^{2}}=\frac{1}{4}m{{r}^{2}}+m{{r}^{2}}=\frac{5m{{r}^{2}}}{4}\]