A rubber cord of density d, Young’s modulus Y and length L is suspended vertically. If the cord extends by a length 0.5 L under its own weight, then L is

Question

A rubber cord of density d, Young’s modulus Y and length L is suspended vertically. If the cord extends by a length 0.5 L under its own weight, then L is (A) (Y/2dg) (B) (Y/dg) (C) (2Y/dg) (D) (dg/2Y)

Tardigrade Admin · Accepted Answer

∵ Young's modulus, Y=( text Stress / text Strain ) Y=(((F/A))/((Δ L)L)) ...(i) ∵ Force exerted due to its own weight =(m g/2) ∴ Y=(((m g/2))/A((0.5)L))=((m g/A L)) So L=(Y/((m g)A L))=(Y/d g)(∵ (m/A L)=d)

Q. A rubber cord of density $d,$ Young’s modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5 L$ under its own weight, then $L$ is

$\frac{Y}{2 d g}$

$\frac{Y}{d g}$

$\frac{2 Y}{d g}$

$\frac{d g}{2 Y}$

$\frac{d g}{Y}$

Q. A rubber cord of density d, Young’s modulus Y and length L is suspended vertically. If the cord extends by a length 0.5L under its own weight, then L is

2dgY​

dgY​

dg2Y​

2Ydg​

Ydg​