When a certain weight is suspended from a lon | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The elongation $l$ of a wire is given by the formula $l = \frac{FL}{AY}$,where $F$ is the force,$L$ is the original length,$A$ is the cross-sectio

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) The elongation $l$ of a wire is given by the formula $l = \frac{FL}{AY}$,where $F$ is the force,$L$ is the original length,$A$ is the cross-sectional area,and $Y$ is Young's modulus.Since $A = \pi r^2 = \pi (d/2)^2$,we have $A \propto d^2$.Given that $F$,$L$,and $Y$ are constant,the elongation $l$ is inversely proportional to the square of the diameter: $l \propto \frac{1}{d^2}$.Let $l_1 = 1 \ cm$ and $d_1 = d$. For the second wire,$d_2 = d/2$.Using the ratio: $\frac{l_2}{l_1} = \left( \frac{d_1}{d_2} ight)^2 = \left( \frac{d}{d/2} ight)^2 = (2)^2 = 4$.Therefore,$l_2 = 4 	imes l_1 = 4 	imes 1 \ cm = 4 \ cm$.

When a certain weight is suspended from a long uniform wire,its length increases by $1 \ cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one,then the increase in length will be ........ $cm$.

Similar Questions

$A$ uniform plank of Young's modulus $Y$ is moved over a smooth horizontal surface by a constant horizontal force $F$. The area of cross-section of the plank is $A$. The compressive strain on the plank in the direction of the force is

$A$ wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$,its length increases by $l$. Another wire of the same material of length $2L$ and radius $2r$ is pulled by a force $2f$. Then the increase in its length will be

Which is more elastic: rubber or steel?

Why are springs made of steel instead of copper?

Vedclass Test Series

Exam Paper Generator

Online Exam Module