SHM

See , the time period of a physical pendulum = 2 π ( Im g d ) ^{1 / 2}

where : -

I = Moment of inertia of the rigid body about the suspension point .

d = Distance from the center of mass of the rigid body to the suspension point .

Now , when the bob is fully filled with water , it behaves like a " solid " sphere , not a hollow one . But , slowly as water drains out , it gradually becomes hollow , thereby changing its time period .

Now , try yourself in proving that , initial time period of the pendulum : -

T₁ = 2 Ï€ ( 7 d5 g ) ^{1 / 2}

And , the final time period : -

T₂ = 2 Ï€ ( 5 d3 g ) ^{1 / 2}

N . B . : - In between these two phenomena , if you want to calculate the time period , then you have to use integration to find out the moment of inertia for a general level of water in the bob . It would then be quite difficult , but certainly not impossible .

ans - time period first increases nd then decreases and finally becomes constant

By the class11 school teachings , we can definitely say that as the water drains out, the centre of mass of the bob gradually moves downwards. Hence, effective length increases.

Since T proportional to √L,
So as the effective length increases, Time Period will increase.

Once the water has gone, the centre of mass moves up, effective length decreases and so the time period returns to what it was when the bob was completely filled with water....