Statement-I:The length of an object is measured with two instruments as l =4.01cm and l =4.009cm, The second instrument has a better resolution
Statement-II: More value is the least count of an instrument, better is the resolution.

Options

A. Statement-1 is true and statement -2 is true
B. Statement -1 is true and statement-2 is false
C. Statement-1 is false and statement -2 is true
D. Statement-1 is false and statement -2 is false

Answer

To analyze the statements given in the question, we will break down the information provided and evaluate the truth of each statement step by step.

### Step 1: Understanding the Measurements
- We have two measurements of length:
- Instrument 1: \( l_1 = 4.01 \, \text{cm} \)
- Instrument 2: \( l_2 = 4.009 \, \text{cm} \)

### Step 2: Identifying the Least Count
- The least count is the smallest value that can be measured by an instrument.
- For Instrument 1, the least count is likely \( 0.01 \, \text{cm} \) (since it can measure to two decimal places).
- For Instrument 2, the least count is likely \( 0.001 \, \text{cm} \) (since it can measure to three decimal places).

### Step 3: Evaluating Statement-I
- Statement-I claims that the second instrument has a better resolution.
- Resolution refers to the ability of an instrument to measure small changes or to distinguish between two closely spaced values.
- Since the least count of Instrument 2 (0.001 cm) is smaller than that of Instrument 1 (0.01 cm), Instrument 2 has a better resolution.
- Therefore, Statement-I is **True**.

### Step 4: Evaluating Statement-II
- Statement-II states that a more value of the least count of an instrument means better resolution.
- This is incorrect because a smaller least count indicates a better resolution.
- Therefore, Statement-II is **False**.

### Conclusion
- Statement-I is True, and Statement-II is False. Thus, the correct answer is that Statement-I is true and Statement-II is false.

### Summary
- **Statement-I**: True (The second instrument has a better resolution due to a smaller least count).
- **Statement-II**: False (A larger least count does not indicate better resolution; rather, a smaller least count does).