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Which one of the following statements is correct? The work done in stretching an elastic string varies
- a)as the square of the extension
- b)as the square root of the extension
- c)linearly with the extension
- d)as the cube root of the extension
Correct answer is option 'A'. Can you explain this answer?
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Which one of the following statements is correct? The work done in st...
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Which one of the following statements is correct? The work done in st...
**Explanation:**
**Stretching of an elastic string:**
When an elastic string is stretched, work is done to overcome the elastic forces within the string. The work done in stretching an elastic string is directly related to the extension of the string.
**Relationship between work done and extension:**
- **a) Work done varies as the square of the extension:**
- The correct statement is that the work done in stretching an elastic string varies as the square of the extension.
- Mathematically, the work done (W) is given by the formula W = kx^2, where k is the spring constant and x is the extension.
- This relationship implies that the work done is proportional to the square of the extension.
- **b) Work done varies as the square root of the extension:**
- This statement is incorrect as the work done does not vary with the square root of the extension.
- The correct relationship is a direct proportionality between the work done and the square of the extension.
- **c) Work done linearly with the extension:**
- This statement is incorrect as the work done does not vary linearly with the extension.
- In the case of stretching an elastic string, the relationship is not linear but rather quadratic.
- **d) Work done varies as the cube root of the extension:**
- This statement is incorrect as the work done does not vary with the cube root of the extension.
- The correct relationship is a square relationship, not a cubic relationship.
**Conclusion:**
The correct statement is that the work done in stretching an elastic string varies as the square of the extension. This relationship is mathematically represented by the formula W = kx^2, where the work done is proportional to the square of the extension.
**Stretching of an elastic string:**
When an elastic string is stretched, work is done to overcome the elastic forces within the string. The work done in stretching an elastic string is directly related to the extension of the string.
**Relationship between work done and extension:**
- **a) Work done varies as the square of the extension:**
- The correct statement is that the work done in stretching an elastic string varies as the square of the extension.
- Mathematically, the work done (W) is given by the formula W = kx^2, where k is the spring constant and x is the extension.
- This relationship implies that the work done is proportional to the square of the extension.
- **b) Work done varies as the square root of the extension:**
- This statement is incorrect as the work done does not vary with the square root of the extension.
- The correct relationship is a direct proportionality between the work done and the square of the extension.
- **c) Work done linearly with the extension:**
- This statement is incorrect as the work done does not vary linearly with the extension.
- In the case of stretching an elastic string, the relationship is not linear but rather quadratic.
- **d) Work done varies as the cube root of the extension:**
- This statement is incorrect as the work done does not vary with the cube root of the extension.
- The correct relationship is a square relationship, not a cubic relationship.
**Conclusion:**
The correct statement is that the work done in stretching an elastic string varies as the square of the extension. This relationship is mathematically represented by the formula W = kx^2, where the work done is proportional to the square of the extension.
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