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The stretch in a steel rod of circular section, having a length ℓ subjected to a tensile load P and tapering uniformly from a diameter d1, at one end to a 'diameter d2 at the other end, is given by
- a)Pl/4Ed1d2
- b)Plπ/Ed1d2
- c)Pl/4E(d1-d2)
- d)4Pl/πEd1d2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The stretch in a steel rod of circular section, having a length subje...
Explanation:
Given:
- Length of the steel rod = L
- Tensile load = P
- Diameter at one end = d1
- Diameter at the other end = d2
- Modulus of elasticity = E
Formula:
The stretch in a tapered steel rod can be calculated using the formula:
ΔL = 4PL / πEd1d2
Explanation of the formula:
- The formula takes into account the length of the rod (L), the applied load (P), the modulus of elasticity (E), and the diameters of the rod at each end (d1 and d2).
- The factor 4/π in the formula accounts for the tapering effect of the rod, as the diameters change from d1 to d2.
Calculation:
Substitute the given values into the formula:
ΔL = (4 * P * L) / (π * E * d1 * d2)
Thus, the correct answer is option 'D': 4PL / πEd1d2.
Given:
- Length of the steel rod = L
- Tensile load = P
- Diameter at one end = d1
- Diameter at the other end = d2
- Modulus of elasticity = E
Formula:
The stretch in a tapered steel rod can be calculated using the formula:
ΔL = 4PL / πEd1d2
Explanation of the formula:
- The formula takes into account the length of the rod (L), the applied load (P), the modulus of elasticity (E), and the diameters of the rod at each end (d1 and d2).
- The factor 4/π in the formula accounts for the tapering effect of the rod, as the diameters change from d1 to d2.
Calculation:
Substitute the given values into the formula:
ΔL = (4 * P * L) / (π * E * d1 * d2)
Thus, the correct answer is option 'D': 4PL / πEd1d2.
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Community Answer
The stretch in a steel rod of circular section, having a length subje...
Explanation:
Given:
Length of steel rod (L), Tensile load (P), Diameter at one end (d1), Diameter at the other end (d2)
Formula for stretch in a tapered steel rod:
The formula for the stretch in a tapered steel rod under a tensile load is given by:
\[ \frac{4PL}{\pi Ed_1d_2} \]
Explanation of the formula:
- P: Tensile load applied on the steel rod
- L: Length of the steel rod
- E: Young's modulus of the material of the steel rod
- d1: Diameter of the steel rod at one end
- d2: Diameter of the steel rod at the other end
Calculation:
- According to the formula, the stretch in a tapered steel rod is directly proportional to the applied load (P), length (L), and inversely proportional to the product of Young's modulus (E) and the product of the diameters at the two ends (d1 and d2).
- The correct formula for the stretch in a tapered steel rod under a tensile load is: \[ \frac{4PL}{\pi Ed_1d_2} \]
- Therefore, the correct answer is option 'D': \[ \frac{4PL}{\pi Ed_1d_2} \]
Given:
Length of steel rod (L), Tensile load (P), Diameter at one end (d1), Diameter at the other end (d2)
Formula for stretch in a tapered steel rod:
The formula for the stretch in a tapered steel rod under a tensile load is given by:
\[ \frac{4PL}{\pi Ed_1d_2} \]
Explanation of the formula:
- P: Tensile load applied on the steel rod
- L: Length of the steel rod
- E: Young's modulus of the material of the steel rod
- d1: Diameter of the steel rod at one end
- d2: Diameter of the steel rod at the other end
Calculation:
- According to the formula, the stretch in a tapered steel rod is directly proportional to the applied load (P), length (L), and inversely proportional to the product of Young's modulus (E) and the product of the diameters at the two ends (d1 and d2).
- The correct formula for the stretch in a tapered steel rod under a tensile load is: \[ \frac{4PL}{\pi Ed_1d_2} \]
- Therefore, the correct answer is option 'D': \[ \frac{4PL}{\pi Ed_1d_2} \]
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The stretch in a steel rod of circular section, having a length subjected to a tensile load P and tapering uniformly from a diameter d1, at one end to a diameter d2 at the other end, is given bya)Pl/4Ed1d2b)Plπ/Ed1d2c)Pl/4E(d1-d2)d)4Pl/πEd1d2Correct answer is option 'D'. Can you explain this answer?
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