When a certain weight is suspended from a long uniform wire, its length increases by one&n

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8.Mechanical Properties of Solids

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

$0.5$

$2$

$4$

$8$

Solution

$\mathrm{y}=\frac{\mathrm{Fl}}{\alpha \Delta \mathrm{l}}$ or $\Delta \mathrm{l} \propto \frac{1}{\alpha} ; \Delta 1 \propto \frac{1}{\mathrm{D}^{2}}$

$\frac{\Delta \mathrm{l}_{2}}{\Delta \mathrm{l}_{1}}=\frac{\mathrm{D}_{1}^{2}}{\mathrm{D}_{2}^{2}}=4$ or $\Delta \mathrm{l}_{2}=4 \Delta \mathrm{l}_{1}=4 \mathrm{cm}$

Standard 11

Physics

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_{1}$ and $Y_{2}$. The combination behaves as a single wire then its Young's modulus is:

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(JEE MAIN-2021)

Explain experimental determination of Young’s modulus.

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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 force required for it is …………$N$ $\left\{Y=10^{10} \,N / m ^2, \alpha=10^{\left.-6 /{ }^{\circ} C \right\}}\right.$

easy

The proportional limit of steel is $8 \times 10^8 \,N / m ^2$ and its Young's modulus is $2 \times 10^{11} \,N / m ^2$. The maximum elongation, a one metre long steel wire can be given without exceeding the elastic limit is …… $mm$

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A structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. A $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress, $(b)$ elongation, and $(c)$ strain on the rod. Young's modulus, of structural steel $1 s 2.0 \times 10^{11} \;N m ^{-2}$

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

Solution

Similar Questions

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are $Y_{1}$ and $Y_{2}$. The combination behaves as a single wire then its Young's modulus is:

Explain experimental determination of Young’s modulus.

The proportional limit of steel is $8 \times 10^8 \,N / m ^2$ and its Young's modulus is $2 \times 10^{11} \,N / m ^2$. The maximum elongation, a one metre long steel wire can be given without exceeding the elastic limit is …… $mm$

A structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. A $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress, $(b)$ elongation, and $(c)$ strain on the rod. Young's modulus, of structural steel $1 s 2.0 \times 10^{11} \;N m ^{-2}$

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