A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):

Question

A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm): (A)  l  (B) 2 l  (C) zero (D)  l /2

Tardigrade Admin · Accepted Answer

Let us consider the length of wire as L and cross-sectional area A, the material of wire has Young's modulus as Y. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6c53a1fe615d51910fa19c555c3144cc-.png" /> Then for 1 st case, Y=(w / A/V L) For 2 nd case, Y=(w / A/2 l' / L) ∴ l'=(l/2) So, total elongation of both sides =2 l'=l

Q. A wire elongates by $l mm$ when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):

$l$

2 $l$

zero

$l$ /2

Q. A wire elongates by lmm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):

l

2 l

zero

l /2

Let us consider the length of wire as L and cross-sectional area A, the material of wire has Young's modulus as Y. Then for 1st case, Y=VLw/A​ For 2nd case, Y=2l′/Lw/A​ ∴l′=2l​ So, total elongation of both sides =2l′=l

Q. A wire elongates by $l mm$ when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):

$l$

2 $l$

$l$ /2