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Question
If all the dimensions of a prismatic bar of square cross-section suspended freely from the ceiling of a roof are doubled then the total elongation produced by its own weight will increase
A.
eight times
B.
four times
C.
three times
D.
two times
Answer ( Option B)

four times

Solution

Elongation due to self-weight of a bar hanging freely:
Where W = self-weight =  r × A ×L × g (r = density, A = cross-sectional area, L = length)
Derivation:
Substituting W = r ALg into the elongation formula:
Notice that A cancels out – elongation due to self-weight depends only on “L2”, not on the cross-sectional area at all.
Now, if all dimensions are doubled:
·  New length L’ = 2L
·  New elongation:

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