The change in length of rod of uniform cross section was found to be 2mm for some applied force. The change in length of the rod of the same material and length but of half the cross section area subjected to the same force will be ------------ mm
Answers
Answer:
In this case, different parts of the rod does not elongate to the same extent. The element closer to the support elongates more as the stress is higher with respect to the elements closer to the free end of the rod. To determine total elongation of the rod, let us consider a small element of differential length dx at a distance x from the free end of the rod, as shown in the Fig. 5.19.
The stress at the position of this element is produced by the weight of the rod of length x lying below it. i.e., (W/L) x.
Therefore, stress at this section
σ=
A
(W/L)x
=
AL
Wx
The elongation dδ produced in the differential element dx is dδ=
Y
σ
dx=
YAL
W
xdx
Thus, total elongation produced in the rod can be calculated as
δ=∫dδ
δ=
YAL
W
∫
0
L
xdx=
YAL
W
[
2
x
2
]
0
L
orσ=
YA
(W/2)L
Explanation:
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