This question has statement `1` and statement `2` . Of the four choice given after the Statement , choose the one that best describe the two Statement .
If the spring `S_(1) `and `S_(2)` of force constant `k_(1)` and `k_(2)` respectively , are streached by the same force , it is found that more work is done on spring `S_(1)` then on spring `S_(2)`
Statement -1: If statement by the same answer work done on `S_(1)` work on `S_(1)` is more then `S_(2)`
Statement - 2 : `k_(1) ltk_(2)`
This question has statement `1` and statement `2` . Of the four choice given after the Statement , choose the one that best describe the two Statement .
If the spring `S_(1) `and `S_(2)` of force constant `k_(1)` and `k_(2)` respectively , are streached by the same force , it is found that more work is done on spring `S_(1)` then on spring `S_(2)`
Statement -1: If statement by the same answer work done on `S_(1)` work on `S_(1)` is more then `S_(2)`
Statement - 2 : `k_(1) ltk_(2)`
If the spring `S_(1) `and `S_(2)` of force constant `k_(1)` and `k_(2)` respectively , are streached by the same force , it is found that more work is done on spring `S_(1)` then on spring `S_(2)`
Statement -1: If statement by the same answer work done on `S_(1)` work on `S_(1)` is more then `S_(2)`
Statement - 2 : `k_(1) ltk_(2)`
A
Statement 1 is false, Statement 2 is true
B
Statement 1 is true, Statement 2 is false
C
Statement 1 is true, Statement 2 is the correct explanation for statement 1
D
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.
Text Solution
AI Generated Solution
The correct Answer is:
To solve the problem, we need to analyze the two statements based on the information provided about the springs and the work done on them.
### Step-by-Step Solution:
1. **Understanding Work Done on Springs**:
- The work done \( W \) on a spring when a force \( F \) is applied can be expressed as:
\[
W = \frac{F^2}{2k}
\]
- Here, \( k \) is the spring constant of the spring, and \( F \) is the force applied.
2. **Given Condition**:
- We are given that the same force \( F \) is applied to both springs \( S_1 \) and \( S_2 \).
- It is stated that more work is done on spring \( S_1 \) than on spring \( S_2 \):
\[
W_1 > W_2
\]
- This implies:
\[
\frac{F^2}{2k_1} > \frac{F^2}{2k_2}
\]
3. **Simplifying the Inequality**:
- Since \( F^2 \) and \( 2 \) are positive constants, we can simplify the inequality:
\[
\frac{1}{k_1} > \frac{1}{k_2}
\]
- This leads us to:
\[
k_1 < k_2
\]
4. **Analyzing the Statements**:
- **Statement 1**: "Work done on \( S_1 \) is more than work done on \( S_2 \)" is true based on our analysis.
- **Statement 2**: "If work done on \( S_1 \) is greater than work done on \( S_2 \), then \( k_1 < k_2 \)" is also true as we derived that \( k_1 < k_2 \).
5. **Conclusion**:
- Both statements are correct based on the analysis we performed. Therefore, the answer to the question is that both statements are true.
### Final Answer:
Both Statement 1 and Statement 2 are correct.
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