question_answer

61. 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 \[\left( \frac{{{\sigma }_{0}}}{r} \right),\]then the radius of gyration of the disc about its axis passing through the centre is :

[JEE Main Held on 12-4-2019 Morning]

A)  \[\frac{a+b}{2}\]                     

B)  \[\frac{a+b}{3}\]

C)  \[\sqrt{\frac{{{a}^{2}}+{{b}^{2}}+ab}{2}}\]          

D)  \[\sqrt{\frac{{{a}^{2}}+{{b}^{2}}+ab}{3}}\]

Correct Answer: D

Solution :

[d]

Radius of gyration