The correct answer is option 2: 2 seconds.
The time period of a simple pendulum is determined by its length and acceleration due to gravity. It is independent of the mass of the bob.
In this scenario, when the wooden bob is replaced with a metallic bob that is twice as heavy, there is no change in the time period. The length of the pendulum and the acceleration due to gravity remain the same.
The reason for this is that the mass of the bob does not affect the gravitational force acting on the pendulum. The force of gravity is proportional to the mass, so the increase in mass is offset by an equal increase in the force acting on it. Therefore, the time period remains unchanged.
Alert - correct answer should be option 2: 2 seconds.