A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching is

Question

A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching is (A) F / 2 l (B) F l (C) 2 F l (D) Fl / 2

Tardigrade Admin · Accepted Answer

Young's modulus Y=(F L/Al) ∴ F=(Y A l/L) dots(i) or dW=F d l=(Y A l(d l)/L) or ∫ d W=(Y A/L) ∫ limits0l l d l=(Y A l2/2 L) or Workdone =(Y A l2/2 L) dots(ii) From (i) and (ii) Workdone =(F l/2)

Q. A wire fixed at the upper end stretches by length $l$ by applying a force $F$ . The work done in stretching is

$F /2 l$

$Fl$

$2 Fl$

Fl / 2

Young's modulus $Y = \frac{F L}{A l}$
$∴ F = \frac{Y A l}{L} \dots (i)$
or $d W = F d l = \frac{Y A l ( d l )}{L}$
or $\int d W = \frac{Y A}{L} 0 \int l l d l = \frac{Y A l ^{2}}{2 L}$
or Workdone $= \frac{Y A l ^{2}}{2 L} \dots (ii)$
From (i) and (ii)
Workdone $= \frac{Fl}{2}$

Q. A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching is

F/2l

Fl

2Fl