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A circular disc of radius b has a hole o...


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 `((sigma_(0))/(r))` then the radius of gyration of the disc about its axis passing through the centre is

A

`(a+b)/(2)`

B

`sqrt((a^(2)+b^(2)+ab)/(2))`

C

`sqrt((a^(2)+b^(2)+ab)/(3))`

D

`(a+b)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C

`l=intdmr^(2)`
`rArr" "int_(a)^(d)((sigma_(0))/(r)2pir dr)r^(2)" "rArr" "l=2sigma_(0)pi(b^(3(-a^(3))))/(3)" "rArr" "l=mk^(2)`
`rArr" "2sigma_(0)pi((b^(3)-a^(3)))/(3)=2sigma_(0)pi(b-a)K^(2)" "rArr" "k=sqrt((a^(2)+b^(2)+ab)/(3))`
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