(B) The formula for elongation $\Delta L$ in a wire is given by $\Delta L = \frac{FL}{AY}$,where $F$ is the load,$L$ is the length,$A$ is the area of

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(B) The formula for elongation $\Delta L$ in a wire is given by $\Delta L = \frac{FL}{AY}$,where $F$ is the load,$L$ is the length,$A$ is the area of cross-section,and $Y$ is the Young's modulus.Given that the load $F$ and length $L$ are the same for both wires,we have $\Delta L \propto \frac{1}{AY}$.Therefore,the ratio of elongation is $\frac{\Delta L_A}{\Delta L_B} = \frac{A_B}{A_A} \times \frac{Y_B}{Y_A}$.Given $\frac{Y_A}{Y_B} = \frac{1}{4}$ and $\frac{A_A}{A_B} = \frac{1}{3}$.Substituting these values,we get $\frac{\Delta L_A}{\Delta L_B} = \frac{3}{1} \times \frac{4}{1} = \frac{12}{1}$.Thus,the ratio is $12: 1$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Medium

Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$,while their areas of cross-section are in the ratio of $1: 3$. If the same amount of load is applied to both the wires,the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of [Assume length of wires $A$ and $B$ are same].

JEE MAIN 2023 All JEE MAIN

A
$36: 1$
B
$12: 1$
C
$1: 36$
D
$12: 1$

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Mechanical Properties of Solids

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Young’s Modulus

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$A$ thin $1 \, m$ long rod has a radius of $5 \, mm$. $A$ force of $50 \, \pi \, kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01 \, mm$,which of the following statements is false?

DifficultJEE MAIN 2016

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$A$ copper wire and an aluminium wire have lengths in the ratio $5: 2$, diameters in the ratio $4: 3$ and forces applied in the ratio $4: 5$. Find the ratio of increase in length of the copper wire to that of the aluminium wire. (Given: $Y_{Cu} = 1.1 \times 10^{11} \text{ Nm}^{-2}$, $Y_{Al} = 0.7 \times 10^{11} \text{ Nm}^{-2}$)

MediumTS EAMCET 2019

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$A$ metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$,the linear stress developed in it is

MediumAIEEE 2011

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Evaluate the following statements:
$(a)$ Young's modulus of a rigid body is .....
$(b)$ $A$ wire increases by $10^{-6}$ times its original length when a stress of $10^8 \ N/m^2$ is applied to it. Calculate its Young's modulus.
$(c)$ The value of Poisson's ratio for steel is ......

Medium

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If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm^2$ is increased from $0^{\circ}C$ to $80^{\circ}C$ and is not allowed to increase in length,then the force required for it is ............$N$ $\{Y=10^{10} \,N/m^2, \alpha=10^{-6}/^{\circ}C\}$

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$A$ thin $1 \, m$ long rod has a radius of $5 \, mm$. $A$ force of $50 \, \pi \, kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01 \, mm$,which of the following statements is false?

$A$ metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$,the linear stress developed in it is

Evaluate the following statements:$(a)$ Young's modulus of a rigid body is .....$(b)$ $A$ wire increases by $10^{-6}$ times its original length when a stress of $10^8 \ N/m^2$ is applied to it. Calculate its Young's modulus.$(c)$ The value of Poisson's ratio for steel is ......

If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm^2$ is increased from $0^{\circ}C$ to $80^{\circ}C$ and is not allowed to increase in length,then the force required for it is ............$N$ $\{Y=10^{10} \,N/m^2, \alpha=10^{-6}/^{\circ}C\}$

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Evaluate the following statements:
$(a)$ Young's modulus of a rigid body is .....
$(b)$ $A$ wire increases by $10^{-6}$ times its original length when a stress of $10^8 \ N/m^2$ is applied to it. Calculate its Young's modulus.
$(c)$ The value of Poisson's ratio for steel is ......