Option 1: If the mass of the bob is doubled without changing the length of the string, the time period of the pendulum will not change. The time period of a simple pendulum is only dependent on the length of the string and the acceleration due to gravity, and not on the mass of the bob.

Option 2: This is the correct answer. When the mass of the bob is doubled and the length of the string is halved, the time period of the pendulum will be halved as well. This is because the time period of a simple pendulum is directly proportional to the square root of the length of the string. Therefore, reducing the length of the string by half will result in the time period being reduced by a factor of (1/√2).

Option 3: If the length of the string is doubled without changing the mass of the bob, the time period of the pendulum will be doubled as well. Again, this is because the time period is directly proportional to the square root of the length of the string.

Option 4: If the length of the string is halved without changing the mass of the bob, the time period of the pendulum will be halved as well. This is the same as the