Question

Example 6. A rubber string 10 mlong is suspended from a
rigid support at its one end. Calculate the extension in the
string due to its own weight. The density of rubber is
1.5 x 103 kg m and Young's modulus for the rubber is
5 x 106 Nm 2. Take g = 10 N kg-1​

Answer 1

Answer:

The weight at any point x from below is ,

10

M

(10−x) where M is mass of string . So , force at any point dx is

F=

l

Mg

(I−X)dx

We know that, Y=

A

F

×

ΔL

l

dl=

AlY

Mg

(l−x)dx

dl=

Y

ρ

dx

(∴ρ=

A.L

M

)

So , Net extension of the rubber due to its own weight =

2×5×10

6

1.5×10

3

×10×100

= 0.15 m

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