Ratio of lengths of two wires A and B of same material is 1 : 2 and ratio of their diameter is 2 : 1

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8.Mechanical Properties of Solids

medium

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

$2:1$

$1:4$

$1:8$

$8:1$

Solution

(c) $l = \frac{{FL}}{{AY}} \Rightarrow l \propto \frac{L}{{{d^2}}}$==>$\frac{{{l_1}}}{{{l_2}}} = \frac{{{L_1}}}{{{L_2}}} \times {\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^2}$

$ = \frac{1}{2} \times {\left( {\frac{1}{2}} \right)^2} = \frac{1}{8}$

Standard 11

Physics

What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times {10^{-5}} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$

hard

The length of metallic wire is $l$. The tension in the wire is $T_1$ for length $l_1$ and tension in the wire is $T_2$ for length $l_2$. Find the original length.

hard

(JEE MAIN-2021)

A steel rod has a radius of $20\,mm$ and a length of $2.0\,m$. A force of $62.8\,kN$ stretches it along its length. Young's modulus of steel is $2.0 \times 10^{11}\,N / m ^2$. The longitudinal strain produced in the wire is $……….\times 10^{-5}$

easy

(JEE MAIN-2023)

The mean distance between the atoms of iron is $3 \times {10^{ – 10}}m$ and interatomic force constant for iron is $7\,N\,/m$The Young’s modulus of elasticity for iron is

medium

The Young's modulus of a rubber string $8\, cm$ long and density $1.5\,kg/{m^3}$ is $5 \times {10^8}\,N/{m^2}$, is suspended on the ceiling in a room. The increase in length due to its own weight will be

medium

(AIIMS-1986)

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

Solution

Similar Questions

What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times {10^{-5}} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$

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