A thick rope of rubber of density 1.5× 103 kg m−3and

Question

A thick rope of rubber of density

1.5 \times 10^{3} k g m^{- 3}

and Young’s modulus

5 \times 10^{6} N m^{- 2},

8m in length is hung from the ceiling of a room, the increase in its length due to its own weight is

Options:

A . 9.6X 10−2 m

B . 19.2 × 10−2 m

C . 9.6× 10−3 m

D . 9.6 m

Answer: Option A
:
A
If A is the area of cross section, d be the density of material and l is lengthof rope
then mass of ropem=Ald
As the weight of the rope acts onthe mid point of the rope

Y = \frac{m g}{A} \times \frac{l}{△ l}

△ l = \frac{m g l}{2 A Y} = \frac{A l p g l}{2 A Y} = \frac{g p l^{2}}{2 Y}

△ l = \frac{9.8 \times 1.5 \times 10^{3} \times 8^{2}}{2 \times 5 \times 10^{6}} = 9.6 \times 10^{- 2} m

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