hey abhijit1 .........

the question tests the concept of " physical pendulum" :

now the time period of a physical pendulum is equal to

T = 2 ( I / mgl)

the theory for this can be read through HCV itself ......

now in the question given , a uniform disc is taken and a physical pendulum is made out using it.......

suppose that the point from where it is suspended is at a distance of a from the centre .......

remember that since it is given that a very small hole is being cut out so we can assume that even after cutting , the centre of mass of the disc remains the same i.e at the centre itself..............

so now for the time period expression we need to have I (moment of inertia about the suspended point)and l ( the distance of the suspended point from the centre of mass)...

I = mr ² / 2 + ma²  ( using the parellel axis theorem)

and l = a

now we need to calculate the minimum value of the time period , so we put

dI/da  ( derivative of I wrt a ) = 0

putting the above values and differentiating we can get

a = r / 2 .............

and putting this value of a , we can get the min time period = T ' = 2 (r2)/g

................keep it cooollll...............