Answer
The time it takes for the ball to attain greatest speed is $0.4s$
Work Step by Step
In a simple pendulum, $$\frac{2\pi}{T}=\sqrt{\frac{g}{L}}$$ $$T=\frac{2\pi}{\sqrt{\frac{g}{L}}}=2\pi\sqrt{\frac{L}{g}}$$
Here, the string's length $L=0.65m$, so the motion's period is $$T=1.62s$$
The ball attains greatest speed at the bottom point of the motion. Since 1 revolution finishes when the ball goes up to its original position, going to the bottom point of the motion is $1/4$ revolution, taking $1/4$ time of the motion's period $T$.
Therefore, the time it takes for the ball to attain greatest speed is $$\frac{T}{4}=0.4s$$
