To solve the problem, we need to analyze the time period of a simple pendulum under different conditions. The original time period \( T \) of the pendulum is given as 1 minute. We will match the scenarios in Column-I with the corresponding outcomes in Column-II.
### Step-by-step Solution:
1. **Time period if the pendulum is oscillated inside a liquid (A)**:
- When a pendulum is submerged in a liquid, it experiences a buoyant force. This reduces the effective gravitational force acting on it.
- If the buoyant force equals the weight of the bob, the effective acceleration due to gravity becomes zero, leading to an infinite time period.
- If the buoyant force is less than the weight, the time period increases compared to the original time period \( T \).
- Therefore, the time period will be **more than \( T \)** (p).
**Match**: A → p
2. **Time period if a constant force less than or equal to the weight of the bob is applied on the bob in a vertically upward direction (B)**:
- If the upward force equals the weight of the bob, the effective gravitational force becomes zero, leading to an infinite time period.
- If the upward force is less than the weight, the effective gravitational force decreases, which increases the time period compared to \( T \).
- Thus, the time period will also be **more than \( T \)** (p).
**Match**: B → p
3. **Time period if the pendulum is oscillated in a moving lift (C)**:
- In a lift moving with constant velocity, the time period remains unchanged, so it equals \( T \).
- If the lift accelerates upward, the effective gravity increases, leading to a decrease in time period (less than \( T \)).
- If the lift accelerates downward, the effective gravity decreases, leading to an increase in time period (more than \( T \)).
- Therefore, the time period can be equal to \( T \), less than \( T \), or more than \( T \) depending on the lift's motion.
**Match**: C → t, s, or q (multiple matches possible)
4. **Time period if its length becomes equal to the radius of the Earth (D)**:
- When the length of the pendulum equals the radius of the Earth, the time period can be calculated using the formula \( T = 2\pi \sqrt{\frac{R}{g}} \).
- This results in a time period that is approximately 1 hour (Q).
**Match**: D → q
### Final Matches:
- A → p (More than T)
- B → p (More than T)
- C → t (T), s (Less than T), or q (More than T)
- D → q (1 hr)
