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JEE Advanced Model Paper 8 with solutions for online practice
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© examsnet.com
Question : 83
Total: 84
A wire of uniform cross-section is hanging vertically and due to its own weight its length changes.There is a point C on the wire such that change in length AC is equal to the change in length BC.Points A, B and C are as shown in the figure. Find
(
√
2
+
1
)
A
C
B
C
Your Answer:
Validate
Solution:
Tension in elementary section of width dx is T = λxg (λ =
mass
length
)
∴ Extension of length x (=Bc) of wire is
Δx =
x
∫
0
(
λ
x
g
)
Y
A
dx =
λ
x
2
g
2
Y
A
..... (i)
⇒ Extension in total length of wire l (= AB) is
2Δx =
λ
l
2
g
2
Y
A
..... (ii)
∴ From equations (i) and (ii) we get x =
l
√
2
A
C
P
C
=
l
−
x
x
= (
√
2
- 1)
© examsnet.com
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