A wire is stretched by 0.01 m by a certain force F. Another wire of same material whose diameter and

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8.Mechanical Properties of Solids

medium

A wire is stretched by $0.01$ $m$ by a certain force $F.$ Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be

$0.005$ $m$

$0.01$ $m$

$0.02$ $m$

$0.002$ $m$

Solution

(a) $l = \frac{{FL}}{{\pi {r^2}Y}}$

$l \propto \frac{L}{{{r^2}}}$ $(Y$ and $F$ are constant$)$

$\frac{{{l_2}}}{{{l_1}}} = \frac{{{L_2}}}{{{L_1}}} \times {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = (2) \times {\left( {\frac{1}{2}} \right)^2} = \frac{1}{2}$

==> ${l_2} = \frac{{{l_1}}}{2} = \frac{{0.01m}}{2} = 0.005m$

Standard 11

Physics

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

easy

In $CGS$ system, the Young's modulus of a steel wire is $2 \times {10^{12}}$. To double the length of a wire of unit cross-section area, the force required is

easy

A meter scale of mass $m$ , Young modulus $Y$ and cross section area $A$ is hanged vertically from ceiling at zero mark. Then separation between $30\ cm$ and $70\ cm$ mark will be 🙁 $\frac{{mg}}{{AY}}$ is dimensionless)

hard

Young’s modulus of perfectly rigid body material is

easy

The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )

medium

(JEE MAIN-2014)

A wire is stretched by $0.01$ $m$ by a certain force $F.$ Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be

Solution

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

In $CGS$ system, the Young's modulus of a steel wire is $2 \times {10^{12}}$. To double the length of a wire of unit cross-section area, the force required is

A meter scale of mass $m$ , Young modulus $Y$ and cross section area $A$ is hanged vertically from ceiling at zero mark. Then separation between $30\ cm$ and $70\ cm$ mark will be 🙁 $\frac{{mg}}{{AY}}$ is dimensionless)

Young’s modulus of perfectly rigid body material is

The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )

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