A circular disc of radius b has a hole of radius ‘a’ at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{{\rm{r}}}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is:

\(\sqrt {\frac{{{a^2} + {b^2} + ab}}{2}} \)

\(\sqrt {\frac{{{a^2} + {b^2} + ab}}{3}} \)

A circular disc of radius b has a hole of radius ‘a’ at its centre

1.	A circular disc of radius b has a hole of radius ‘a’ at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{{\rm{r}}}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is:
A.	\(\sqrt {\frac{{{a^2} + {b^2} + ab}}{2}} \)
B.	\(\frac{{a + b}}{2}\)
C.	\(\sqrt {\frac{{{a^2} + {b^2} + ab}}{3}} \)
D.	\(\frac{{a + b}}{3}\)
Answer» D. \(\frac{{a + b}}{3}\)

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A circular disc of radius b has a hole of radius ‘a’ at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{{\rm{r}}}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is:

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