The ratio of the lengths of two wires A and B | vedclass

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

Question

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

Vedclass · Accepted Answer

$1:8$

Vedclass · Answer

(C) The formula for the extension $l$ of a wire is given by $l = \frac{FL}{AY}$,where $F$ is the force,$L$ is the original length,$A$ is the cross-sectional area,and $Y$ is Young's modulus.Since the material is the same,$Y$ is constant. The area $A = \pi r^2 = \pi (d/2)^2$,so $A \propto d^2$.Thus,$l \propto \frac{L}{d^2}$.Given $\frac{L_A}{L_B} = \frac{1}{2}$ and $\frac{d_A}{d_B} = \frac{2}{1}$.The ratio of increase in lengths is $\frac{l_A}{l_B} = \frac{L_A}{L_B} 	imes \left( \frac{d_B}{d_A} ight)^2$.Substituting the values: $\frac{l_A}{l_B} = \frac{1}{2} 	imes \left( \frac{1}{2} ight)^2 = \frac{1}{2} 	imes \frac{1}{4} = \frac{1}{8}$.Therefore,the ratio is $1:8$.

The ratio of the lengths of two wires $A$ and $B$ of the same material is $1 : 2$ and the ratio of their diameters is $2 : 1$. If they are stretched by the same force,then the ratio of the increase in their lengths will be:

Similar Questions

The negation of the statement ''If $I$ become a teacher,then $I$ will open a school'',is

Which crop developed by mutation breeding shows resistance to yellow mosaic virus?

What is the undifferentiated mass of cells in tissue culture called?

Which one of the following is most acidic?

The process requiring absorption of energy is

Vedclass Test Series

Exam Paper Generator

Online Exam Module