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The elongation of a conical bar under its own weight is ......that of prismatic bar of the same length.
- a)equal to
- b)half
- c)one-third
- d)two-third
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The elongation of a conical bar under its own weight is ......that of ...
Conical bar/Prismatic Bar.
= (wl^2/6E) / (wl^2/2E),
=1/3.
Most Upvoted Answer
The elongation of a conical bar under its own weight is ......that of ...
Elongation of Conical Bar under its own weight
- When a conical bar is subjected to its own weight, it undergoes elongation due to the axial stress developed in it.
- This elongation is different from that of a prismatic bar of the same length, as the cross-sectional area of the conical bar varies along its length.
- The elongation of a conical bar under its own weight is given by the formula:
ΔL = (ρghL^3)/(3E)
where,
ΔL = elongation of the bar
ρ = density of the material
g = acceleration due to gravity
h = height of the bar
L = length of the bar
E = Young's modulus of elasticity
Comparison with Prismatic Bar
- In a prismatic bar of the same length, the cross-sectional area remains constant along its length.
- The elongation of a prismatic bar under its own weight is given by the formula:
ΔL = (ρgWL^3)/(3AE)
where,
W = weight of the bar
A = cross-sectional area of the bar
Conclusion
- Comparing the two formulas, we can see that the elongation of a conical bar under its own weight is one-third that of a prismatic bar of the same length, as the formula for elongation of a prismatic bar involves the weight of the bar.
- Hence, the correct answer is option 'C': one-third.
- When a conical bar is subjected to its own weight, it undergoes elongation due to the axial stress developed in it.
- This elongation is different from that of a prismatic bar of the same length, as the cross-sectional area of the conical bar varies along its length.
- The elongation of a conical bar under its own weight is given by the formula:
ΔL = (ρghL^3)/(3E)
where,
ΔL = elongation of the bar
ρ = density of the material
g = acceleration due to gravity
h = height of the bar
L = length of the bar
E = Young's modulus of elasticity
Comparison with Prismatic Bar
- In a prismatic bar of the same length, the cross-sectional area remains constant along its length.
- The elongation of a prismatic bar under its own weight is given by the formula:
ΔL = (ρgWL^3)/(3AE)
where,
W = weight of the bar
A = cross-sectional area of the bar
Conclusion
- Comparing the two formulas, we can see that the elongation of a conical bar under its own weight is one-third that of a prismatic bar of the same length, as the formula for elongation of a prismatic bar involves the weight of the bar.
- Hence, the correct answer is option 'C': one-third.
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Community Answer
The elongation of a conical bar under its own weight is ......that of ...
The elongation in prismatic bar is YL^2/2E where Y is gamma and called as weight density whereas for a conical bar the elongation is YL^2/6E just divide the thing.
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