Given below are two statements :
Statement I : A second's pendulum has a time period of 1 second.
Statement II : It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options given below:

Options

A. Both Statement I and Statement II are false.
B. Statement I is false but Statement II is true
C. Statement I is true but Statement II is false
D. Both Statement I and Statement II are true.

Answer

To solve the problem, we need to analyze the two statements regarding a second's pendulum.

### Step 1: Understanding the Second's Pendulum
A second's pendulum is defined as a pendulum that has a time period of 2 seconds. This means it takes 2 seconds to complete one full oscillation (from one extreme position to the other and back).

**Hint:** Recall the definition of a second's pendulum and its time period.

### Step 2: Evaluating Statement I
**Statement I:** "A second's pendulum has a time period of 1 second."
- This statement is incorrect. The time period of a second's pendulum is actually 2 seconds, not 1 second.

**Hint:** Remember that the time period refers to the time taken for one complete oscillation.

### Step 3: Evaluating Statement II
**Statement II:** "It takes precisely one second to move between the two extreme positions."
- This statement is correct. Since the time period of the pendulum is 2 seconds, it takes half of that time (1 second) to move from one extreme position to the other.

**Hint:** Consider how the motion of the pendulum is divided into halves: one half for each extreme position.

### Step 4: Conclusion
Based on the evaluations:
- Statement I is false.
- Statement II is true.

Thus, the correct answer is that the first statement is false and the second statement is true.

**Final Answer:** The correct option is that Statement I is false and Statement II is true.